Mayo, a 6-foot-5 inch guard for Southern California and the third overall selection by the Timberwolves, was dealt to the Grizzlies with guards Marko Jaric and Greg Buckner and forward Antoine Walker.
Love, a 6-foot-10 inch power forward from UCLA and the draft's fifth overall pick by the Grizzlies, went to Minnesota along with shooting guard Mike Miller and forwards Brian Cardinal and Jason Collins.
Both Love and Mayo were freshmen last college basketball season.
"I just wanted to hear my name called and be part of the NBA," Mayo said shortly after he was picked Thursday by the Timberwolves. "It didn't matter if it was a big-market organization, small-market, medium-market."
Jaric averaged 8.3 points a game last season, Bruckner averaged 4 points while playing for his fourth NBA team and Miller has a career average of 16.4 points a game.