AWS CDK: how to target API Gateway API from Route53

With aws-cdk v1 should be able to do the following:

const zone = route53.HostedZone.fromHostedZoneAttributes(this, 'ZenithWebFoundryZone', {
  hostedZoneId: 'ZXXXXXX04V8134',
  zoneName: 'zenxxxxxxfoundry.com' // your zone name here
});

new route53.ARecord(this, 'BlogAPIRecord', {
  zone,
  recordName: 'xxxxxx.zenxxxxxxfoundry.com',
  target: route53.RecordTarget.fromAlias({
    bind() {
      return {
        dnsName: 'd-xxxxxxy00g.execute-api.ap-southeast-2.amazonaws.com', // Specify the applicable domain name for your API.,
        hostedZoneId: 'XXXX', // Specify the hosted zone ID for your API.
      };
    },
  }),
});

If your API is in the same stack/code base you can get the dnsName and hostedZoneId from it (it's a CF attribute).

Otherwise refer to DNSName and HostedZoneId in the AWS::Route53::RecordSet AliasTarget documentation.

Note: the hostedZoneId for your alias record is not the same as the hosted zone id of your own zone.

I was facing the same issue using cdk 1.36.1 and managed to solve it using a new Custom Domain Name in ApiGateway, together withBasePath Mapping and then adding a CName record in an existing hosted zone on route53 pointing to the new custom domain:

import {BasePathMapping, DomainName, EndpointType, LambdaRestApi} from '@aws-cdk/aws-apigateway';
import {Certificate} from '@aws-cdk/aws-certificatemanager';
import {HostedZone, CnameRecord} from '@aws-cdk/aws-route53'

// First create a custom domain:
const customDomain = new DomainName(this, 'customDomain', {
      domainName: 'api.xxxxxxx.com',
      certificate: Certificate.fromCertificateArn(this, 'ACM_Certificate', ACM_CERTIFICATE_ARN),
      endpointType: EndpointType.EDGE
});

// create a new ApiGateway instance and associate a lambda function with it:
const api = new LambdaRestApi(this, 'MainGatewayEndpoint', {
      handler: toyFunction,
});

// Associate the Custom domain that we created with new APIGateway using BasePathMapping:
new BasePathMapping(this, 'CustomBasePathMapping', {
      domainName: custom,
      restApi: api
});

// Get a reference to AN EXISTING hosted zone using the HOSTED_ZONE_ID. You can get this from route53
const hostedZone = HostedZone.fromHostedZoneAttributes(this, 'HostedZone', {
      hostedZoneId: PROD_HOSTED_ZONE_ID,
      zoneName: 'xxxxxxx.com'
});

// Finally, add a CName record in the hosted zone with a value of the new custom domain that was created above:
new CnameRecord(this, 'ApiGatewayRecordSet', {
      zone: hostedZone,
      recordName: 'api',
      domainName: customDomain.domainNameAliasDomainName
});