Because the director, Frank Darabont, didn't feel comfortable handing over the reins to anyone else, he wrote the screenplay himself as well. Frequently this is a sign of someone with an overinflated ego and zip talent, especially considering that Darabont had really no prior success that would justify his taking full creative control. But boy, he knew what he was doing.
Both of his first two major films, Shawshank and The Green Mile, were nominated for Best Picture, and he also picked up a screenplay nomination for both. There are several lines and scenes that have since become ingrained in the public consciousness, and there are few more memorable quotes than, "Get busy living, or get busy dying." Sometimes you just have to pull a Rocky and kick all the other cooks out of the kitchen.
Darabont has found more success as a director than a writer in the years since, but he did write for a little show called The Walking Dead after he co-created the series in 2010, and that show has picked up more than a fan or two in the time since its inception. Apparently, most of the people on that show have chosen to "get busy dying."