I work for a small company that up until recently had a small number of dedicated servers hosted by a hosting company on Public IP's. To manage all of our internal websites we used SSH tunnels and apache website serving only to localhost.

Recently as we are have been expanding the amount of tunnels that we have to use is starting to get a bit crazy and we are looking for another solution. We want someone to access one server and have access to the other servers(on public IP's) over a secure connection. All servers run either Ubuntu or Debian. 

What kind of solutions should we be looking at? Can we setup a VPN to improve on this setup?