The 31-year-old was released by West Brom and joins Bolton on a free transfer.
Andrews has signed a three-year contract with Bolton.
“We are pleased to have been able to bring in Keith early in the transfer window as there were a number of clubs interested in signing him,” Bolton boss Owen Coyle told the the club’s official website.
“He is highly experienced, both in domestic and international football. He will bring strength, competition and a goalscoring threat to our midfield.”
Andrews added: “It (the Championship) is a very tough league, but if you have the right characters and the dressing room, you can be successful.
“Looking at our squad, I believe we have a fantastic group of players to tackle the Championship.
“I’m sure there will be a few new signings and fresh faces too, and that can only help the current squad. We are certainly geared up to be fighting for promotion. I was aware of the manager’s interest before the European Championships and I was obviously very flattered by that.
“Every time I have come across the manager, he always seems like a very positive person.
“He spoke to me at length and highlighted his vision for the club, saying how he wanted to get back up to the Premier League at the first opportunity.”
