The film, which will be shot on location in Scotland, will tell the story of the father and son from St Andrews who helped develop the game in the late 1800s.
The two men won eight Open Championship titles - four each - between 1861 and 1872.
Connery said: “I am incredibly passionate and excited to tell this story. It is a story that is truly close to my heart as I grew up with my father on a golf course and I have a home an hour from St Andrews.”
Casting on the film, based on the award-winning book Tommy’s Honor by author Kevin Cook, is underway, and filming is set to begin in the spring.