The Scotland international has moved for an undisclosed fee, believed to be in the region of £4million.
Announcing the news on their official website, the Potters said the fact the transfer had been sealed before midday meant they were hopeful Adam would be available for the Barclays Premier League clash with Wigan at the DW Stadium.
Manager Tony Pulis told the club's official website: "It's no secret we've been looking to bring more goals to the squad and Charlie is a fantastic signing in that respect."
Adam said: "I'm delighted to be here and to be given the opportunity to work with the club, the manager and the players. This club's on the up and it's great to be a part of it. I hope I can help them to improve upon the success which has been achieved over the past few years.
"Hopefully, we can have a successful time together. I'm looking forward to the chance of playing in front of their passionate supporters."
And Bolton have completed the signing of Liverpool midfielder Jay Spearing on a season-long loan.
The 23-year-old joins the club with exceptional pedigree having already made over 50 appearances for the Premier League side.
"We have been in the market for a player of this kind for a long time and Jay is someone that we have always had an eye on," manager Owen Coyle told the club's official website.
"He was previously never available and, indeed, played the majority of games in Liverpool's first team last season in the Premier League.
"We did everything we could to bring Jay to the football club and so we are thrilled to bring in a player of his calibre.
"He is a young player that is driven, who is a terrific passer of the ball. He has a real desire to do well and has all the attributes that we crave at Bolton Wanderers."