There is a contradiction between the title and the body of your question. Since the title makes no real sense (a client connecting to a client?), I'll assume your question is the one from your body, emphasis mine:
I want to have a way to prove to servers behind the proxy they are actually receiving a request from the proxy server and not from something else.
If both the proxy server and the servers are a part of your network, then the app servers can simply match the IP address of the request with the IP address of the proxy server. Of course, you should be sure that you don't have a rogue DHCP on your network, and that your proxy server has a static IP address no other machine could have if the proxy is down. If you are unsure about the network configuration, ServerFault may help.
If the proxy is outside your network, but you're able to control its configuration, you may ask the server to inject the secret key in the HTTP headers of the request. Obviously, HTTPS between the proxy and the server is mandatory to prevent the leakage of the secret key.
Following the comments, it appears that, indeed, the goal is to be able to identify whether the request was sent directly or through a proxy—any proxy. I imagine that the OP wants to throw away users who are accessing the website through a proxy server (by the way, if this is the real purpose of the question, the goal is itself subject to discussion).
In this case, the technique which would work most of the time consists of checking the presence of HTTP headers which are usually added by proxy servers. It should be noted that some proxies may decide not to add any headers; similarly, nothing prevents the original requester from adding those headers without being a proxy.
Another approach would be to continuously index IP addresses of proxy servers used by the bad guys (if this is the actual problem you're trying to solve). The benefit is that legit users—the ones who are behind a corporate firewall, for example—are not affected. The drawback is that it's relatively easy for an attacker to swap a proxy server when the one he uses is blocked.