Villa was the first player to sign for incoming MLS franchise New York City, penning a three-year deal ahead of the club's inaugural season in 2015.
Spain's all-time leading goalscorer arrives in the United States on the back of Atletico Madrid's triumphant 2013-14 La Liga campaign.
And the 32-year-old is relishing the opportunity to make his mark in MLS alongside team-mate Frank Lampard, having won every trophy on offer in Spain, as well as the UEFA Champions League.
"I've done a lot in Europe already, a very good career; an opportunity to start from zero, to start over again is something I thought was exciting," Villa told reporters on Thursday.
"I want to leave a winning legacy.
"One of hard work and dedication so people remember the name David Villa."
Villa will link up with Melbourne, who are also bankrolled by Premier League champions Manchester City, on loan until December before returning to New York for the club's debut season.