diff --git a/packages/@aws-cdk/aws-stepfunctions/README.md b/packages/@aws-cdk/aws-stepfunctions/README.md
index b7c54e428d877..b2deba80f5356 100644
--- a/packages/@aws-cdk/aws-stepfunctions/README.md
+++ b/packages/@aws-cdk/aws-stepfunctions/README.md
@@ -673,6 +673,22 @@ new cloudwatch.Alarm(this, 'ThrottledAlarm', {
 });
 ```
 
+## Logging
+
+Enable logging to CloudWatch by passing a logging configuration with a
+destination LogGroup:
+
+```ts
+const logGroup = new logs.LogGroup(stack, 'MyLogGroup');
+
+new stepfunctions.StateMachine(stack, 'MyStateMachine', {
+    definition: stepfunctions.Chain.start(new stepfunctions.Pass(stack, 'Pass')),
+    logs: {
+      destinations: logGroup,
+      level: stepfunctions.LogLevel.ALL,
+    }
+});
+```
 
 ## Future work
 
diff --git a/packages/@aws-cdk/aws-stepfunctions/lib/state-machine.ts b/packages/@aws-cdk/aws-stepfunctions/lib/state-machine.ts
index efb9f5659c31d..e60c2a29a3eb3 100644
--- a/packages/@aws-cdk/aws-stepfunctions/lib/state-machine.ts
+++ b/packages/@aws-cdk/aws-stepfunctions/lib/state-machine.ts
@@ -1,5 +1,6 @@
 import * as cloudwatch from '@aws-cdk/aws-cloudwatch';
 import * as iam from '@aws-cdk/aws-iam';
+import * as logs from '@aws-cdk/aws-logs';
 import { Construct, Duration, IResource, Resource, Stack } from '@aws-cdk/core';
 import { StateGraph } from './state-graph';
 import { CfnStateMachine } from './stepfunctions.generated';
@@ -24,6 +25,56 @@ export enum StateMachineType {
     STANDARD = 'STANDARD'
 }
 
+/**
+ * Defines which category of execution history events are logged.
+ *
+ * @see https://docs.aws.amazon.com/step-functions/latest/dg/cloudwatch-log-level.html
+ *
+ * @default ERROR
+ */
+export enum LogLevel {
+    /**
+     * No Logging
+     */
+    OFF = 'OFF',
+    /**
+     * Log everything
+     */
+    ALL = 'ALL',
+    /**
+     * Log all errors
+     */
+    ERROR= 'ERROR',
+    /**
+     * Log fatal errors
+     */
+    FATAL = 'FATAL'
+}
+
+/**
+ * Defines what execution history events are logged and where they are logged.
+ */
+export interface LogOptions {
+  /**
+   * The log group where the execution history events will be logged.
+   */
+  readonly destination: logs.ILogGroup;
+
+  /**
+   * Determines whether execution data is included in your log.
+   *
+   * @default true
+   */
+  readonly includeExecutionData?: boolean;
+
+  /**
+   * Defines which category of execution history events are logged.
+   *
+   * @default ERROR
+   */
+  readonly level?: LogLevel;
+}
+
 /**
  * Properties for defining a State Machine
  */
@@ -60,6 +111,13 @@ export interface StateMachineProps {
      * @default StateMachineType.STANDARD
      */
     readonly stateMachineType?: StateMachineType;
+
+    /**
+     * Defines what execution history events are logged and where they are logged.
+     *
+     * @default No logging
+     */
+    readonly logs?: LogOptions;
 }
 
 /**
@@ -132,11 +190,37 @@ export class StateMachine extends StateMachineBase {
 
         this.stateMachineType = props.stateMachineType ? props.stateMachineType : StateMachineType.STANDARD;
 
+        let loggingConfiguration: CfnStateMachine.LoggingConfigurationProperty | undefined;
+        if (props.logs) {
+            const conf = props.logs;
+            loggingConfiguration = {
+                destinations: [{ cloudWatchLogsLogGroup: { logGroupArn: conf.destination.logGroupArn } }],
+                includeExecutionData: conf.includeExecutionData,
+                level: conf.level || 'ERROR'
+            };
+            // https://docs.aws.amazon.com/step-functions/latest/dg/cw-logs.html#cloudwatch-iam-policy
+            this.addToRolePolicy(new iam.PolicyStatement({
+              effect: iam.Effect.ALLOW,
+              actions: [
+                'logs:CreateLogDelivery',
+                'logs:GetLogDelivery',
+                'logs:UpdateLogDelivery',
+                'logs:DeleteLogDelivery',
+                'logs:ListLogDeliveries',
+                'logs:PutResourcePolicy',
+                'logs:DescribeResourcePolicies',
+                'logs:DescribeLogGroups'
+              ],
+              resources: ['*']
+            }));
+        }
+
         const resource = new CfnStateMachine(this, 'Resource', {
             stateMachineName: this.physicalName,
             stateMachineType: props.stateMachineType ? props.stateMachineType : undefined,
             roleArn: this.role.roleArn,
             definitionString: Stack.of(this).toJsonString(graph.toGraphJson()),
+            loggingConfiguration
         });
 
         resource.node.addDependency(this.role);
diff --git a/packages/@aws-cdk/aws-stepfunctions/package.json b/packages/@aws-cdk/aws-stepfunctions/package.json
index 8d53040da7428..c2941b6f2546e 100644
--- a/packages/@aws-cdk/aws-stepfunctions/package.json
+++ b/packages/@aws-cdk/aws-stepfunctions/package.json
@@ -74,6 +74,7 @@
     "@aws-cdk/aws-cloudwatch": "0.0.0",
     "@aws-cdk/aws-events": "0.0.0",
     "@aws-cdk/aws-iam": "0.0.0",
+    "@aws-cdk/aws-logs": "0.0.0",
     "@aws-cdk/core": "0.0.0",
     "constructs": "^2.0.0"
   },
@@ -82,6 +83,7 @@
     "@aws-cdk/aws-cloudwatch": "0.0.0",
     "@aws-cdk/aws-events": "0.0.0",
     "@aws-cdk/aws-iam": "0.0.0",
+    "@aws-cdk/aws-logs": "0.0.0",
     "@aws-cdk/core": "0.0.0",
     "constructs": "^2.0.0"
   },
diff --git a/packages/@aws-cdk/aws-stepfunctions/test/test.state-machine.ts b/packages/@aws-cdk/aws-stepfunctions/test/test.state-machine.ts
index 2aab5ea1070d8..ab1aaf1b46263 100644
--- a/packages/@aws-cdk/aws-stepfunctions/test/test.state-machine.ts
+++ b/packages/@aws-cdk/aws-stepfunctions/test/test.state-machine.ts
@@ -1,4 +1,5 @@
 import { expect, haveResource } from '@aws-cdk/assert';
+import * as logs from '@aws-cdk/aws-logs';
 import * as cdk from '@aws-cdk/core';
 import { Test } from 'nodeunit';
 import * as stepfunctions from '../lib';
@@ -63,5 +64,66 @@ export = {
         }));
 
         test.done();
-    }
+    },
+
+    'log configuration'(test: Test) {
+        // GIVEN
+        const stack = new cdk.Stack();
+
+        // WHEN
+        const logGroup = new logs.LogGroup(stack, 'MyLogGroup');
+
+        new stepfunctions.StateMachine(stack, 'MyStateMachine', {
+            definition: stepfunctions.Chain.start(new stepfunctions.Pass(stack, 'Pass')),
+            logs: {
+              destination: logGroup,
+              level: stepfunctions.LogLevel.FATAL,
+              includeExecutionData: false
+            }
+        });
+
+        // THEN
+        expect(stack).to(haveResource('AWS::StepFunctions::StateMachine', {
+            DefinitionString: '{"StartAt":"Pass","States":{"Pass":{"Type":"Pass","End":true}}}',
+            LoggingConfiguration: {
+                Destinations: [{
+                    CloudWatchLogsLogGroup: {
+                        LogGroupArn: {
+                            'Fn::GetAtt': ['MyLogGroup5C0DAD85', 'Arn']
+                        }
+                    }
+                }],
+                IncludeExecutionData: false,
+                Level: 'FATAL'
+            }
+        }));
+
+        expect(stack).to(haveResource('AWS::IAM::Policy', {
+            PolicyDocument: {
+                Statement: [{
+                    Action: [
+                        'logs:CreateLogDelivery',
+                        'logs:GetLogDelivery',
+                        'logs:UpdateLogDelivery',
+                        'logs:DeleteLogDelivery',
+                        'logs:ListLogDeliveries',
+                        'logs:PutResourcePolicy',
+                        'logs:DescribeResourcePolicies',
+                        'logs:DescribeLogGroups'
+                    ],
+                    Effect: 'Allow',
+                    Resource: '*'
+                }],
+                Version: '2012-10-17'
+            },
+            PolicyName: 'MyStateMachineRoleDefaultPolicyE468EB18',
+            Roles: [
+                {
+                    Ref: 'MyStateMachineRoleD59FFEBC'
+                }
+            ]
+        }));
+
+        test.done();
+    },
 };