Fortunately, no one buys into that theory any more. That was started almost 100 years after the murders by someone who claimed he'd read Dr. Gull's private papers in which Gull stated that Eddy, who was his patient, was Jack the Ripper. But since no one else has ever seen these papers (what a surprise), that's just assertion. These papers are also supposed to say that Eddy had syphilis and died not of influenza as announced but of "softening of the brain". But Gull was hardly in a position to know anything about Eddy's death, since he died two years before Eddy did. The whole thing's a crock. Eddy wasn't even in town for most of the murders; on the day of the double murder (Stride and Eddowes), he was in Scotland having lunch with his grandma.
In Clarence, a biography of Eddy, Michael Harrison fingers poet James Kenneth Stephen as the Ripper. Stephen's physician was...guess who. I imagine that's why Dr. Gull himself came under suspicion -- because his name keeps popping up so much.