Having had other offers, the 34-year-old had been waiting on a final decision new club since being released by Grimsby Town at the end of last season following 57 appearances for the Mariners.
“I am very happy to get the deal done at Linfield, ” he said.
“I am looking forward to this experience along with the opportunity to play at the historic Windsor Park,” he said.
“ A big club comes with big ambitions and this move suits me great at this stage of my career.
“David Healey has obviously been a fantastic striker himself and he says he is going to add to my game and teach me some new things.
“Eventually I will explore Belfast. The team and all staff have made me feel very welcome. This is a great opportunity for me and I can't wait to get started.
“I would like to mention my family and close friends supporting me in my decision after turning down various opportunities else where in England. “Me and my two boys can’t wait to put on the current Champions shirt with great pride.”
Green began his professional career at Newport County in 2005 and his clubs have included Oxford United, Birmingham City and two spells at the Stags.
“He's a player with great experience across various clubs,” said Blues boss David Healy.
“We've been tracking him for a little while and he had options to join several other clubs.
“I've spoken to quite a few contacts in England about him and everything I've heard about him has been positive.”
Green's most productive goalscoring spell came during his first stint at Mansfield between 2012 and 2013 when he notched 40 goals in 62 games and helped them to the Blue Square Conference title.
That earned him a move to Championship club Birmingham City but a knee injury ruined that and he returned to Mansfield in 2015 before stints at Lincoln City, Salford City and Grimsby, where he scored five goals in his two seasons.
Linfield, who have already exited both of this season's European competitions, begin their Danske Bank Premiership fixtures against Crusaders on Saturday. Green will join the squad for the game subject to international clearance.