Championship side Bristol City have won the race for the Sudan-born ace, making him their seventh signing of a busy summer following the arrivals of Marley Watkins, Adam Webster, Gustav Engvall, Hakeeb Adelakun, Andreas Weimann and Jack Hunt.
Speaking to his new side's official website, Eisa said: "I am very excited. I can't wait to get started. It's a massive club with a large fanbase and I want to do as well as I can for the team.
"I will get my head down, work hard and see where we can finish. I want us to get promoted, although I won't get carried away. I had a good season for Cheltenham last year, the best of my career. I have to thank the club because without them I wouldn't be here."
Eisa only joined Cheltenham from non-league Greenwich Borough last summer.