"Blackburn Rovers are delighted to announce the appointment of Sam Allardyce as manager with immediate effect," the club said on its website.
The 54-year-old replaces Paul Ince, who was sacked on Tuesday after six successive Premier League defeats.
Blackburn, who host fellow strugglers Stoke City on Saturday, are second from bottom.
Allardyce, who will hold a news conference on Thursday, said he was delighted to accept the job.
Asked whether he would be given money to strengthen the squad, Allardyce told Sky Sports News: "We'll wait and see."
Allardyce made his name at Bolton after taking over in October 1999. He guided the club to the first division playoffs and an FA Cup semi-final in his first campaign before winning promotion to the Premier League a season later.
Allardyce resigned two matches before the end of the 2006-07 season and was appointed Newcastle manager in May last year.
Despite a promising start, heavy home defeats by Portsmouth and Liverpool led to him leaving in January this year.
Former England midfielder Ince, 41, was appointed by Rovers on a three-year deal in June, replacing his former Manchester United team mate Mark Hughes who left to take over at Manchester City.
Rovers began the season with a win at Everton but picked up just two further league victories, the last in late September.
Allardyce has also managed Blackpool and Notts County.
Earlier on Wednesday, former Blackburn manager Graeme Souness had ruled himself out of a return to Ewood Park.
"I'm afraid you are talking to the wrong man," he told the Lancashire Telegraph.
"I don't know anything and have had no contact at all from Blackburn Rovers. I'm not your man, I can definitely say that."
BLACKBURN FANS! Check FourFourTwo.com’s ever-expandinginterviews archivefor more stuff to read:
My Secret Vice Sam Allardyce
Boy's A Bit Special Danny Simpson
What Happened Next? David May
Plus! Rate Rovers players (and others) on Talentspotter
BOLTON FANS! Check FourFourTwo.com’s ever-expandinginterviews archivefor more stuff to read:
My Secret Vice Sam Allardyce
Boy's A Bit Special Fabrice Muamba, Danny Guthrie
What Happened Next? Tony Cunningham
Plus! Rate Wanderers players (and others) on Talentspotter
