The 37-year-old was a member of the Chelsea side that won the English Premier League twice in a row in 2004-05 and 2005-06 and also won La Liga and Champions League with Barcelona in 2008-09.
The Iceland international made his national senior team debut at the age of 17 in 1996 when he came on as a half-time substitute for his own father, Arnor.
Expressing his joy on joining FC Pune, Gudjohnsen said in a release, "There were other clubs interested in me but when FC Pune City show their interest, intent and plans, I knew this was it. I have the confidence of the coach and will ensure that they find it difficult to leave me out."
"Everyone needs to be motivated to succeed, and I have the same aim here. I love the sport. I still love going to training every day."
He scored 78 goals in 263 appearances for Chelsea. He recently was in action at Euro 2016 in France.
FC Pune's head coach Antonio Habas was excited with the new joining.
"Eidur's has experience of playing at highest levels and a professional motivation to succeed. I've admired him from afar for many years and am very excited at the prospect of us working together for the benefit of FC Pune City," Habas said in the release.
