Both players have signed three-year deals with the Trotters.
Centre-back Knight, who has won two England caps, joined Villa in the summer of 2007 from Fulham in a £3.5million deal but struggled for regular first-team football, starting just 13 Premier League games last season.
Wales international Ricketts, who can play on the left or the right of a back four, started 27 of the Tigers' Premier League games in their debut season in the top flight.
They are Wanderers boss Gary Megson's third and fourth signings of the summer, with the club having brought in Sean Davis after his contract at Portsmouth expired and also defender Paul Robinson from West Brom.
Both Knight and Ricketts joined up with the Trotters squad yesterday, where they are currently on tour in Germany.