The 22-year-old midfielder has signed a three-year deal, with the option of a further 12 months after limited opportunities at the Reebok.
While hailing the player's attitude, Bolton boss Owen Coyle believes it would not have been fair to keep hold of him.
He told the club's official website: "Chris is a great lad but unfortunately there is plenty of competition here in the position that he plays.
"As a young, enthusiastic player making his way in the game then it wouldn't have been fair for us to keep him as he wouldn't have got as many chances to play as he would have liked.
"I wish him nothing but good luck at Blackpool because it is a fantastic opportunity for him to play in the Premier League."
Basham made his debut for Bolton against Sunderland in November 2008 and went on to make 19 appearances for the club, with his only goal coming against Chelsea at Stamford Bridge in April 2009.