The 29-year-old striker joins the Trotters on a two-year deal following two seasons with the Foxes in which he scored 15 times in 49 appearances after a move from Premier League side Everton.
Beckford spent most of last term on loan at Huddersfield and found the net eight times in 21 Championship outings as the Terriers narrowly avoided relegation.
His move to the Reebok Stadium comes two weeks after personal terms were agreed and a medical passed at the Lancashire club.
Bolton boss Dougie Freedman played alongside Beckford during the pair's days at Leeds and is fully aware of what the marksman will bring to his side.
"We have worked very hard in order to bring Jermaine to the club, it has been a long winded signing," Freedman told Wanderers' official website.
"It has been out in the press for the last few weeks but Jermaine is someone I know and I have previously played alongside him so I know his character.
"He is a goal scorer and in certain games that last season we dominated we weren't clinical enough and that is what Jermaine brings."
- Sports & Recreation
- Dougie Freedman