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."