That would be essentially Cloudflare’s basic setup, but I presume you are talking about a host which runs an API so you wont be able to take advantage of Cloudflare’s caching, will you?
In that case you could look into Cloudflare’s load balancer, which offers AFAIK geographically distributed connections of that sort. Alternatively you could also look into Argo Tunnel which would allow your different instances to connect to their (and in turn the users’) nearest datacentre.