The four-year deal is worth $38.4 million, sources told ESPN.
Sources told ESPN's Brian Windhorst that the Cleveland Cavaliers and the Bucks have had some sign-and-trade talks on Dellavedova but have made no traction.
The Bucks are confident the Cavs will not match the offer sheet, sources said. The Cavaliers have three days to do so once the offer sheet is signed. July 7 is the first day that free agents may sign deals.
LeBron James tweeted on Friday afternoon to congratulate Dellavedova and wish him luck.
The Bucks have signaled their interest in Dellavedova for some time. They sent scouts to Cleveland during the playoffs to evaluate Dellavedova, and coach Jason Kidd attended a Finals game.
Earlier Friday, the Bucks agreed with free agent forwardMirza Teletovic on a three-year deal.
Information from ESPN's Zach Lowe was used in this report.