The Demons will hand over picks 61 and 79 to Carlton for Garlett, while they will get back the Blues' pick 83.
Garlett requested a trade to the Demons on Tuesday after 107 games and 183 goals for the Blues.
Garlett kicked just 12 goals in nine games in 2014, but he has twice managed more than 40 goals in a season (2011 and 2013).
Essendon was also in the race to land Garlett, but he ultimately chose the Demons after meeting with the club's senior players and coach Paul Roos' desire to add him to the forward line.
Demons football manager Josh Mahoney said the small forward position was recognised as a hole the club needed to fill in 2015.
"It was a role that we identified that we wanted to fill during the trade period as a small, crumbing forward," Mahoney told melbournefc.com.au.
"His record prior to last year stacks up with the best small forwards in the competition – he averages nearly two goals and three-and-a-half tackles per game.
"We think that he can be a dangerous option for us in the forward line, working in tandem with Jay Kennedy-Harris and Dean Kent."
Blues football manager Andrew McKay said the club was pleased to allow Garlett a "fresh start".
"Jeff leaves us with our best wishes for the future," McKay told carltonfc.com.au.
"It was time for him to have a fresh start and we are pleased to have been able to facilitate that by reaching agreement on a trade with Melbourne."
Melbourne has not had a leading goalkicker boot more than 29 goals in a season since Liam Jurrah kicked 40 in 2011.