The 28-year-old will now seek a third club having played 122 games in eight seasons for the Demons and another 23 at Geelong in 2003-04.
Moloney won Melbourne's best-and-fairest award in 2011 and polled 19 Brownlow votes but fell out of favour with new coach Mark Neeld this season.
The Demons thanked Moloney for his contributions and wished him well in his future endeavours.
"We respect Brent's position, and the fact that he has been up front with us throughout the process," Neeld said.
"This is the new world of AFL free agency - Brent is a restricted free agent and the rules allow him to explore these opportunities. We wish him well for the future."
Technically, Melbourne would be able to keep Moloney, as a restricted free agent, if they matched any offer he received from a rival club, but expressed their willingness on Tuesday to let him go.
Moloney must wait for the inaugural free agency period on October 1 to negotiate with a new club, but thanked Melbourne for their support.
"I have enjoyed my eight seasons at the club, but it's now time to pursue other opportunities," Moloney said."I am grateful for everything the club has given me. I have built great relationships with Melbourne people and I wish all involved the best for the future."