Route53 is basically the solution you describe with DNS records, and you could build out anycast DNS servers yourself if you wanted. The main thing to be aware

Route53 is basically the solution you describe with DNS records, and you could build out anycast DNS servers yourself if you wanted. The main thing to be aware of is that not all clients respect TTLs. We set a 30s ttl and see a 99% switchover in about 60s but if you have some control over the clients you could probably go lower.