The 31-year-old has signed an 18-month contract at Upton Park to end a miserable spell at Anfield.
Cole told his new club's official website: "It is a great move for me. 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."
Cole emerged from the club's academy to sign professional terms in 1998 and helped them win the FA Youth Cup the following year, becoming a firm fans' favourite before leaving for Chelsea in 2003, when he became one of their first signings following Roman Abramovich's takeover of the club.
There, he won eight major trophies including three Premier League titles, was named in the Professional Footballers Association team of the year in 2006 and has won 56 full England caps.
But after joining Liverpool as a free agent, he was sent off on his Premier League debut and missed a penalty in his next appearance, a Europa League qualifying match against Trabzonspor. The poor start set the tone for a Reds career hampered by form and fitness problems and he was allowed to spend last season on loan at Lille.
He scored nine goals in 42 appearances for the French club and will have the opportunity to further rebuild his career at the club where he first made his name.
Cole said: "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.
"Sam (Allardyce, manager) didn't have to sell me the club for me to come back. 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."
The warm reception he received from the Upton Park crowd when he returned with Liverpool last month, which he reciprocated by not celebrating his goal in the Reds' 3-2 win, was also a factor in his return.
"It was a big thing in me coming back, the fact that everybody here wants me to do well," Cole added. "The fans have always been great for me, whenever I have been back and also when I've been in the area visiting family.
"I feel like I owe the club a little bit as well because if it wasn't for West Ham I wouldn't be a footballer. This club's great youth-team coaches taught me the trade."
The Hammers lie 11th in the Premier League table after 20 games and Cole is optimistic about their prospects for the remainder of the campaign.
"The first season in the Premier League is always the toughest one and the boys have done brilliant to get 26 points on the board," he said. "We would like to match that in the second half of the season and crack on from there.
"We have got a lot of England internationals and a good strong squad here, so our home form is going to be vital."
Hammers boss Sam Allardyce was obviously delighted with his new signing.
"It's a good one for us. I think that somebody as talented as Joe and as enthusiastic about playing football and not all about money, as most transfers seem to be about today, is a pleasure to bring back to the club and give the opportunity he is looking for.
"I think that we will give him that and hopefully he will grasp it with both hands and produce some of the outstanding ability and quality that we know he has and do that for us during the period of time that his contact is with us.
"If we can extract the best out of him again then it will be a fantastic signing for us at West Ham.
"He is somebody that is coming back home from where he started. He has realised his dreams here of being a footballer and it's great to have secured the deal and really great that he chose us.
The former Bolton and Blackburn chieftain doesn't believe that Cole's lack of first-team action will hinder his progress at the club, despite not starting a Premier League game this season.
"It's nice to have a player who has played 56 times for England. He's just into his thirties so I think there is an awful lot of football left in him. He hasn't being playing regularly enough since his move to Liverpool which frustrated him.
"He feels he needs a break to get somewhere else and recreate himself and I think we have got the back-up services and the staff behind the scenes to help him do that. For us it is a great move and hopefully it is for him.
"Extra quality in the team is always important. Joe's main strength lies in possession and his ability to open teams up and beat individuals is a key element and that is what we will be looking for."