The 31-year-old who was released by West Brom after joining the club in January has agreed a three-year deal with the Wanderers.
The former Blackburn and Hull City midfielder had a number of clubs reportedly interested in his services after playing all three group games for Ireland at Euro 2012.
Bolton manager Owen Coyle expressed his pleasure at capturing Andrews early in the transfew window.
"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," 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 enjoyed a successful loan spell at Championship side Ipswich in the first half of last season and the Irishman hopes he can succeed at the level with Bolton.
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."