The 29-year-old's move to London further strengthens the Hammers, who have already brought in Newcastle captain Kevin Nolan and Stoke's Abdoulaye Faye to Upton Park this summer as they bid to make an instant return to the Premier League.
Taylor passed a medical on Friday but the deal, understood to be for four years, could not be finalised until Saturday afternoon as Bolton were returning from a pre-season tour in the United States.
This is a great opportunity to come and play for a fantastic football club," Taylor told the club's official website.
"This is a big club with a lot of heritage. It is a new challenge for me and obviously I want to be part of something special and, from the outset, it looks like I will find that here."
Taylor joined Bolton from Portsmouth in January 2008 and rapidly established himself as a key first-team player at the Reebok Stadium.
The move to West Ham will see the left-sided midfielder drop down a division but Taylor insists he is relishing the challenge of getting the recently-relegated club back to the top flight at the first attempt.
"Ultimately it is a huge football club and I want to play my part if I can," he said.
"There were never any second thoughts about coming here.
"It is a big challenge for me which I am looking forward to, to be part of helping the team get back up to the Premier League and do that as soon as possible.
"I see this as a very positive move for me. I don't expect to be playing Championship football for more than one season if I am being totally honest.
"I just want to get stuck in and start playing. I think it is going to be a great season."
Taylor also admitted manager Allardyce formed a key part in his decision to move to east London.
"I have had good conversations with the gaffer, he is such a positive person," he added.
"I think you can see already the aura around the place and the quality of players he has brought in to add to the players already here.
"From a totally impartial point of view, I couldn't see anything other than that I was coming to a great football club and wanted to be part of it."