Cole made just 42 appearances for Liverpool since joining the club from Chelsea in July 2010.
The midfielder joins the Hammers on a free transfer.
“It is a great move for me,” the 31-year-old told West Ham’s official website.
“Coming back here brings back all the memories of the pitches I learnt how to play on. This is where I learnt my trade and I’m happy to have another chance to be here. I’ve always loved West Ham and I hope I can give the club a few memorable seasons.
“The timing was right for me to come back and I’m happy. I’m back in London and I’m delighted to be here. I want to be here and I want to make an impact.
“The place has not changed much to look at, but I think Sam has done a great job with the team. A few years ago, the club was in a bad way and Sam has done brilliantly. All in all, it will always be West Ham and the history will always be here and everywhere I go around the world, people love West Ham. Everywhere I go, people know me for having started here.”
Cole added: “Sam didn’t have to sell me the club for me to come back. For me, I have had 18 months at Liverpool where I haven’t played much football and Sam wants to play me. I’m going to need games to get back to my best, but I want to play football and come here and help the team to make an impact.
“I could see from the outside what a great bunch of lads we have here and there is a great spirit. I’m excited.”
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As always it is the so called “big clubs” that have splashed the most cash in the transfer window so far this summer. Manchester United or City? Arsenal or Tottenham? Who are the winners and losers of the transfer window so far?
Being an amiable guy is good for you and Jurgen Klopp is living proof.