Dudley does not have an official title yet, but Burke said the former Blackhawks assistant GM would be a premier talent evaluator with the Leafs.
Dudley, 62, lost his GM job with the Thrashers when the club moved to Winnipeg, and the new owners chose Kevin Cheveldayoff as their new general manager. Several clubs contacted Dudley.
"There were a lot of people who talked to me," Dudley told ESPN.com. "But partly because it was Brian and partly because it was the Leafs, it was very appealing to be part of that resurgence. The Leafs are going to have success in Toronto and to be around and be part of it all will be exciting to say the least."
Pierre LeBrun covers the NHL for ESPN.com. Information from The Associated Press was used in this report.