diff --git a/qiskit/transpiler/passes/layout/sabre_layout.py b/qiskit/transpiler/passes/layout/sabre_layout.py
index 312cd51c73bd..7771578f40f2 100644
--- a/qiskit/transpiler/passes/layout/sabre_layout.py
+++ b/qiskit/transpiler/passes/layout/sabre_layout.py
@@ -319,8 +319,12 @@ def to_partial_layout(layout):
         if (prev_final_layout := self.property_set.get("final_layout", None)) is None:
             self.property_set["final_layout"] = final_layout
         else:
-            self.property_set["final_layout"] = final_layout.compose(
-                prev_final_layout, out_dag.qubits
+            # The "final layout" can be thought of as a "comes from" permutation that you apply at
+            # the end of the circuit to invert the routing.  So if there's an existing one, what we
+            # apply at the end of the circuit needs to set the circuit qubits so they "come from"
+            # the previous one, then those "come from" the one we've just added.
+            self.property_set["final_layout"] = prev_final_layout.compose(
+                final_layout, out_dag.qubits
             )
         return out_dag
 
diff --git a/qiskit/transpiler/passes/routing/basic_swap.py b/qiskit/transpiler/passes/routing/basic_swap.py
index e1245051d42b..70b20eba0a87 100644
--- a/qiskit/transpiler/passes/routing/basic_swap.py
+++ b/qiskit/transpiler/passes/routing/basic_swap.py
@@ -117,8 +117,12 @@ def run(self, dag):
         if self.property_set["final_layout"] is None:
             self.property_set["final_layout"] = current_layout
         else:
-            self.property_set["final_layout"] = current_layout.compose(
-                self.property_set["final_layout"], dag.qubits
+            # The "final layout" can be thought of as a "comes from" permutation that you apply at
+            # the end of the circuit to invert the routing.  So if there's an existing one, what we
+            # apply at the end of the circuit needs to set the circuit qubits so they "come from"
+            # the previous one, then those "come from" the one we've just added.
+            self.property_set["final_layout"] = self.property_set["final_layout"].compose(
+                current_layout, dag.qubits
             )
 
         return new_dag
@@ -160,7 +164,11 @@ def _fake_run(self, dag):
         if self.property_set["final_layout"] is None:
             self.property_set["final_layout"] = current_layout
         else:
-            self.property_set["final_layout"] = current_layout.compose(
-                self.property_set["final_layout"], dag.qubits
+            # The "final layout" can be thought of as a "comes from" permutation that you apply at
+            # the end of the circuit to invert the routing.  So if there's an existing one, what we
+            # apply at the end of the circuit needs to set the circuit qubits so they "come from"
+            # the previous one, then those "come from" the one we've just added.
+            self.property_set["final_layout"] = self.property_set["final_layout"].compose(
+                current_layout, dag.qubits
             )
         return dag
diff --git a/qiskit/transpiler/passes/routing/lookahead_swap.py b/qiskit/transpiler/passes/routing/lookahead_swap.py
index 4c6462c04a87..98d09874eb14 100644
--- a/qiskit/transpiler/passes/routing/lookahead_swap.py
+++ b/qiskit/transpiler/passes/routing/lookahead_swap.py
@@ -172,8 +172,12 @@ def run(self, dag):
         if self.property_set["final_layout"] is None:
             self.property_set["final_layout"] = current_state.layout
         else:
-            self.property_set["final_layout"] = current_state.layout.compose(
-                self.property_set["final_layout"], dag.qubits
+            # The "final layout" can be thought of as a "comes from" permutation that you apply at
+            # the end of the circuit to invert the routing.  So if there's an existing one, what we
+            # apply at the end of the circuit needs to set the circuit qubits so they "come from"
+            # the previous one, then those "come from" the one we've just added.
+            self.property_set["final_layout"] = self.property_set["final_layout"].compose(
+                current_state.layout, dag.qubits
             )
 
         if self.fake_run:
diff --git a/qiskit/transpiler/passes/routing/sabre_swap.py b/qiskit/transpiler/passes/routing/sabre_swap.py
index bbc7a16c5da9..2868bac197b9 100644
--- a/qiskit/transpiler/passes/routing/sabre_swap.py
+++ b/qiskit/transpiler/passes/routing/sabre_swap.py
@@ -245,6 +245,10 @@ def run(self, dag):
         self.property_set["final_layout"] = (
             layout
             if (prev := self.property_set["final_layout"]) is None
-            else layout.compose(prev, dag.qubits)
+            # The "final layout" can be thought of as a "comes from" permutation that you apply at
+            # the end of the circuit to invert the routing.  So if there's an existing one, what we
+            # apply at the end of the circuit needs to set the circuit qubits so they "come from"
+            # the previous one, then those "come from" the one we've just added.
+            else prev.compose(layout, dag.qubits)
         )
         return dag
diff --git a/releasenotes/notes/fix-final-layout-8b027fb01e831ef9.yaml b/releasenotes/notes/fix-final-layout-8b027fb01e831ef9.yaml
new file mode 100644
index 000000000000..c8d5311905d2
--- /dev/null
+++ b/releasenotes/notes/fix-final-layout-8b027fb01e831ef9.yaml
@@ -0,0 +1,11 @@
+---
+fixes:
+  - |
+    Built-in transpiler passes that set the ``final_layout`` property will now correctly handle
+    updating this field if it was already set.  This can be observed as the method
+    :attr:`.TranspileLayout.routing_permutation` now returning a correct permutation after running
+    more than one pass that sets ``final_layout``.
+
+    This did not affect any normal calls to :func:`.transpile` or :func:`.generate_preset_pass_manager`
+    using Qiskit's built-in plugins; no pipeline constructed in this form would attempt to set
+    ``final_layout`` more than once.
diff --git a/test/python/compiler/test_transpiler.py b/test/python/compiler/test_transpiler.py
index e5a0f4340d8d..202c78db2858 100644
--- a/test/python/compiler/test_transpiler.py
+++ b/test/python/compiler/test_transpiler.py
@@ -18,6 +18,7 @@
 import math
 import os
 import sys
+import random
 from logging import StreamHandler, getLogger
 from unittest.mock import patch
 import numpy as np
@@ -62,6 +63,7 @@
     ECRGate,
     HGate,
     IGate,
+    PermutationGate,
     PhaseGate,
     RXGate,
     RYGate,
@@ -85,7 +87,7 @@
 from qiskit.providers.options import Options
 from qiskit.quantum_info import Operator, random_unitary
 from qiskit.utils import should_run_in_parallel
-from qiskit.transpiler import CouplingMap, Layout, PassManager
+from qiskit.transpiler import CouplingMap, Layout, PassManager, passes
 from qiskit.transpiler.exceptions import TranspilerError, CircuitTooWideForTarget
 from qiskit.transpiler.passes import BarrierBeforeFinalMeasurements, GateDirection, VF2PostLayout
 
@@ -2729,6 +2731,50 @@ def callback(**kwargs):
         self.assertTrue(vf2_post_layout_called)
         self.assertEqual([2, 1, 0], _get_index_layout(tqc, qubits))
 
+    @data("sabre", "lookahead", "basic")
+    def test_final_layout_combined_correctly(self, routing):
+        """Test that multiple `final_layout`s are combined correctly."""
+        generators = {
+            "sabre": lambda cmap, seed: passes.SabreSwap(cmap, seed=seed, trials=1),
+            "lookahead": lambda cmap, _seed: passes.LookaheadSwap(cmap),
+            "basic": lambda cmap, seed: passes.BasicSwap(cmap),
+        }
+        make_routing_pass = generators[routing]
+
+        def random_line(num_qubits, rng):
+            line = list(range(num_qubits))
+            rng.shuffle(line)
+            out = CouplingMap([[a, b] for a, b in zip(line[:-1], line[1:])])
+            out.make_symmetric()
+            return out
+
+        rng = random.Random(0)
+        num_qubits = 5
+
+        # This is just loads of stars, so routing has to work for it.
+        qc = QuantumCircuit(num_qubits)
+        for i in range(num_qubits):
+            for j in range(num_qubits):
+                if i == j:
+                    continue
+                qc.cx(i, j)
+        # ... and the mirror, so the circuit implements the identity.
+        qc.barrier()
+        qc.compose(qc.inverse(), qc.qubits, inplace=True)
+
+        # Routing needs a layout set, and we don't want qubit relabelling to mess with our test.
+        pm = PassManager([passes.SetLayout(list(range(num_qubits))), passes.ApplyLayout()])
+        # Now we route the circuit to several different coupling maps in a row, so we generate lots
+        # of routing permutations, and each pass needs to combine them.
+        pm += PassManager([make_routing_pass(random_line(num_qubits, rng), i) for i in range(5)])
+        out = pm.run(qc)
+
+        # The invariant of `routing_permutation` is that you're supposed to be able to append it as
+        # a permutation and it will "undo" the effects.  We already know our circuit implements the
+        # identity.
+        out.append(PermutationGate(out.layout.routing_permutation()), out.qubits)
+        self.assertEqual(Operator(out), Operator(np.eye(2**num_qubits)))
+
     @data(0, 1, 2, 3)
     def test_annotations_survive(self, optimization_level):
         """Test that custom annotations survive a full transpile."""