The 32-year-old had been training with the Scottish champions for much of the last four weeks and has done enough to convince manager Ronny Deila to add him to his squad.
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Cole was a free agent after being released by West Ham United at the end of last season. He began his career at Chelsea, where he was part of their Premier League winning squad in 2006, and had loan spells at Wolves, Charlton and Aston Villa while with the Stamford Bridge club.
He joined West Ham in 2006 and spent nine seasons at the club, during which time he earned seven full England caps.
Sunderland, Bournemouth and Bolton Wanderers were all credited with an interest in Cole since his release by West Ham but he has opted to continue his career with a fresh challenge in Scotland.
He will be able to make his debut for Deila’s side in their next Premiership fixture against bottom of the table Dundee United at Celtic Park on Sunday.
Cole is not eligible to play for Celtic during their Europa League group stage campaign but can be added to their European squad in the second half of the season if they reach the knockout stages of the tournament.
A statement from the Parkhead side said: “Celtic are delighted to announce that striker Carlton Cole has signed for the club until the summer of 2017.”