The 30-year-old has been a fixture in the Dragons side since joining them from St George Illawarra in time for their second season in 2007 and recently became the first non-French player to make 100 Super League appearances for them.
"My partner and I have decided to move back to Australia at the end of the season to be close to our family," Greenshields said. "It has been an extremely hard decision to make as I feel a part of me is French and I still have so many friends here."
He added: "I wanted to let (coach) Trent (Robinson) and (chairman) Bernard Guasch know early so they could find a replacement."
Greenshields is the leading try scorer in the seven-year history of the Catalan club with 62 touchdowns in 119 Super League appearances and earned a place in the Super League Dream Team in 2008.
He became eligible to represent France two years ago but has not yet played for them.