The 30-year-old initially left the club earlier this summer, but has failed to get a new club.
Cole returned to train with West Ham last month and has now agreed an initial three-month deal with the club.
Cole will be able to play against Manchester City this Saturday evening.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.