Kelly burst into tears as he received his award Sunday night, thanking the Birmingham Repertory Theatre for their support during a "terrible time," the Times of London reported Monday.
"Without them," Kelly said, "I would never have got through this year."
Kelly won the award for playing Lenny in John Steinbeck's classic, a role the actor took in February 2003, three weeks after being arrested on allegations he sexually abused a boy in the 1970s. Kelly was cleared of the charges.
The top winner of the night was "Jerry Springer -- The Opera," which took home four awards, a rare feat for a production that grossed less than $10 million. In addition to winning best new musical, David Bedella won for best actor in a musical.