The 30-year-old defender moves to Ewood Park on a two-year contract, but the fee is undisclosed.
Chimbonda first went to White Hart Lane when he was transferred from Wigan in summer 2006. He left Spurs for an ill-fated sixth-month spell with Sunderland last summer only to return to the club in January.
However, he has fallen down the pecking order in recent months behind the likes of Vedran Corluka, Alan Hutton and new signing Kyle Naughton.
Allardyce said of his latest capture: "We've got the deal done. We've got an experienced player who's desperate to play football again, having missed it at Spurs.
"We all know his favourite position is right-back. We're well covered there, but he can play centre-back and left-back.
"He was eager to get away from Tottenham, because he hasn't played enough games for them and he just wants to play football.
"When you meet someone who tells you they just want to play football it's a good thing from the start.
"When you see what he's achieved in his early days at Wigan and Tottenham we want him to come and emulate that at Blackburn, whichever position we pick him in."