diff --git a/yarn-project/end-to-end/src/e2e_avm_simulator.test.ts b/yarn-project/end-to-end/src/e2e_avm_simulator.test.ts
index 6691ad45c34..3acebe956a0 100644
--- a/yarn-project/end-to-end/src/e2e_avm_simulator.test.ts
+++ b/yarn-project/end-to-end/src/e2e_avm_simulator.test.ts
@@ -33,6 +33,14 @@ describe('e2e_avm_simulator', () => {
       avmContract = await AvmTestContract.deploy(wallet).send().deployed();
     });
 
+    describe('Assertions', () => {
+      it('Processes assertions in the PXE', async () => {
+        await expect(avmContract.methods.assert_nullifier_exists(123).simulate()).rejects.toThrow(
+          "Assertion failed: Nullifier doesn't exist!",
+        );
+      });
+    });
+
     describe('Gas metering', () => {
       it('Tracks L2 gas usage on simulation', async () => {
         const request = await avmContract.methods.add_args_return(20n, 30n).create();
diff --git a/yarn-project/simulator/src/avm/avm_machine_state.ts b/yarn-project/simulator/src/avm/avm_machine_state.ts
index eeb490b291b..ca4b5e72056 100644
--- a/yarn-project/simulator/src/avm/avm_machine_state.ts
+++ b/yarn-project/simulator/src/avm/avm_machine_state.ts
@@ -138,12 +138,12 @@ export class AvmMachineState {
     let revertReason = undefined;
     if (this.reverted && this.output.length > 0) {
       try {
+        // We remove the first element which is the 'error selector'.
+        const revertOutput = this.output.slice(1);
         // Try to interpret the output as a text string.
-        revertReason = new Error(
-          'Reverted with output: ' + String.fromCharCode(...this.output.slice(1).map(fr => fr.toNumber())),
-        );
+        revertReason = new Error('Assertion failed: ' + String.fromCharCode(...revertOutput.map(fr => fr.toNumber())));
       } catch (e) {
-        revertReason = new Error('Reverted with non-string output');
+        revertReason = new Error('<no output>');
       }
     }
     return new AvmContractCallResults(this.reverted, this.output, revertReason);
diff --git a/yarn-project/simulator/src/avm/avm_simulator.test.ts b/yarn-project/simulator/src/avm/avm_simulator.test.ts
index a625e63697f..73afe6c07ed 100644
--- a/yarn-project/simulator/src/avm/avm_simulator.test.ts
+++ b/yarn-project/simulator/src/avm/avm_simulator.test.ts
@@ -111,7 +111,7 @@ describe('AVM simulator: transpiled Noir contracts', () => {
     const results = await new AvmSimulator(context).executeBytecode(bytecode);
 
     expect(results.reverted).toBe(true);
-    expect(results.revertReason?.message).toEqual("Reverted with output: Nullifier doesn't exist!");
+    expect(results.revertReason?.message).toEqual("Assertion failed: Nullifier doesn't exist!");
     expect(results.output).toEqual([
       new Fr(0),
       ...[..."Nullifier doesn't exist!"].flatMap(c => new Fr(c.charCodeAt(0))),
diff --git a/yarn-project/simulator/src/avm/opcodes/external_calls.test.ts b/yarn-project/simulator/src/avm/opcodes/external_calls.test.ts
index ae81b5afc48..bf052349410 100644
--- a/yarn-project/simulator/src/avm/opcodes/external_calls.test.ts
+++ b/yarn-project/simulator/src/avm/opcodes/external_calls.test.ts
@@ -315,7 +315,7 @@ describe('External Calls', () => {
       expect(context.machineState.halted).toBe(true);
       expect(context.machineState.getResults()).toEqual({
         reverted: true,
-        revertReason: new Error('Reverted with output: assert message'),
+        revertReason: new Error('Assertion failed: assert message'),
         output: returnData.map(f => f.toFr()),
       });
     });
diff --git a/yarn-project/simulator/src/public/transitional_adaptors.ts b/yarn-project/simulator/src/public/transitional_adaptors.ts
index 5e241a6a315..ae317f9006e 100644
--- a/yarn-project/simulator/src/public/transitional_adaptors.ts
+++ b/yarn-project/simulator/src/public/transitional_adaptors.ts
@@ -1,8 +1,10 @@
 // All code in this file needs to die once the public executor is phased out in favor of the AVM.
-import { UnencryptedFunctionL2Logs } from '@aztec/circuit-types';
+import { type SimulationError, UnencryptedFunctionL2Logs } from '@aztec/circuit-types';
 import {
+  type AztecAddress,
   CallContext,
   FunctionData,
+  type FunctionSelector,
   type Gas,
   type GasSettings,
   type GlobalVariables,
@@ -10,11 +12,12 @@ import {
 } from '@aztec/circuits.js';
 import { Fr } from '@aztec/foundation/fields';
 
+import { extractCallStack } from '../acvm/index.js';
 import { type AvmContext } from '../avm/avm_context.js';
 import { AvmExecutionEnvironment } from '../avm/avm_execution_environment.js';
 import { type AvmContractCallResults } from '../avm/avm_message_call_result.js';
 import { Mov } from '../avm/opcodes/memory.js';
-import { createSimulationError } from '../common/errors.js';
+import { ExecutionError, createSimulationError } from '../common/errors.js';
 import { type PublicExecution, type PublicExecutionResult } from './execution.js';
 
 /**
@@ -72,6 +75,29 @@ export function createPublicExecution(
   return execution;
 }
 
+export function processRevertReason(
+  revertReason: Error | undefined,
+  contractAddress: AztecAddress,
+  functionSelector: FunctionSelector,
+): SimulationError | undefined {
+  if (!revertReason) {
+    return undefined;
+  }
+  if (revertReason instanceof Error) {
+    const ee = new ExecutionError(
+      revertReason.message,
+      {
+        contractAddress,
+        functionSelector,
+      },
+      extractCallStack(revertReason),
+      { cause: revertReason },
+    );
+
+    return createSimulationError(ee);
+  }
+}
+
 export function convertAvmResultsToPxResult(
   avmResult: AvmContractCallResults,
   startSideEffectCounter: number,
@@ -81,6 +107,7 @@ export function convertAvmResultsToPxResult(
 ): PublicExecutionResult {
   const endPersistableState = endAvmContext.persistableState;
   const endMachineState = endAvmContext.machineState;
+
   return {
     ...endPersistableState.transitionalExecutionResult, // includes nestedExecutions
     execution: fromPx,
@@ -92,7 +119,11 @@ export function convertAvmResultsToPxResult(
       endPersistableState.transitionalExecutionResult.allUnencryptedLogs,
     ),
     reverted: avmResult.reverted,
-    revertReason: avmResult.revertReason ? createSimulationError(avmResult.revertReason) : undefined,
+    revertReason: processRevertReason(
+      avmResult.revertReason,
+      endAvmContext.environment.address,
+      fromPx.functionData.selector,
+    ),
     startGasLeft: startGas,
     endGasLeft: endMachineState.gasLeft,
     transactionFee: endAvmContext.environment.transactionFee,