The Australian-born half-back put pen to paper in a two year contract after previously spending two years at Craven Park.
Tomkins said: “Blake is a great signing for us. He is still relatively young. He is the kind of players we want at the club; we don’t want any signings to be a quick fix.
“I believe he can fill the gap left at half back. He is a quality player and he should fit well into the Wigan mould.”
Green also plyed his trade for Parramatta Eels, Cronulla Sharks and Canterbury Bulldogs, making over 40 appearances in the NRL before moving to Super League and Hull KR for the start of the 2011 season.
He is likely to partner Matty Smith in the halves at the DW Stadium next season. Smith, 25, joined the Warriors from Salford towards the back end of the 2012 campaign.