Patricia Cornwell first theorized that Walter Sickert was Jack the Ripper in her 2002 book, Portrait of a Killer: Jack the Ripper—Case Closed, which I've read and found as convincing (or more convincing) than other Jack the Ripper theories. Although the article doesn't go into detail, the Daily Mail reports that Cornwell has uncovered additional evidence which suggests that Sickert was the killer and linking him to the Royal Family. Unfortunately, we will have to wait for Cornwell to publish her findings next year.
Cornwell's theory is based on Sickert's later interest in, and paintings of, the Ripper murders. Also, she tracked down some details concerning Sickert's travels and personal habits that seemed to coincide with the Ripper killings, as well as similar killings elsewhere. A summary of her ideas are here.
In 2001, the Guardian ran an article critical of Cornwell's theory. And this Wikipedia article on Cornwell's book briefly lists some other arguments.