The 57-year-old Chilean, Jose Mourinho's predecessor at Real, replaces Jesualdo Ferreira, who was sacked after only three months in the job on Tuesday with the Andalusian club languishing 18th in the 20-team La Liga.
GEAR:Save 10% on La Liga shirts here, courtesy of online retailer Kitbag
"The Chilean coach Manuel Pellegrini will be presented as new head coach tomorrow," the club said in a statement.
Local media quoted Pellegrini saying he had been offered a five-year deal but had opted for a three-year contract.
"I am excited and very pleased," he said. "I feel capable of turning this situation around and hopefully the team will recover."
Pellegrini made his mark in Spain with Villarreal between 2004 and 2009, turning a small, unfashionable club into a regular participant in European competitions.
ATTRACTIVE FOOTBALL
He won widespread praise for bringing through young talent and for playing attractive, attacking football, leading them to runners-up spot behind Real Madrid in La Liga in 2007/08.
He also steered Villarreal to the Champions League semi-finals in 2006 and the quarter-finals in 2009.
Real Madrid bought him out of his contract in June 2009 but he only lasted a season before being replaced by Mourinho, despite achieving a record points tally for the club of 96 with a team that scored 102 goals in 38 matches.
Real had spent 250 million euros on new players such as Cristiano Ronaldo, Kaka and Karim Benzema but failed to win any silverware, finishing second behind Barcelona in the league and failing to progress beyond the last 16 in the Champions League for a sixth straight season.
"The club (Malaga) is growing and has a very impressive project," Pellegrini was quoted as saying in Thursday's edition of sports daily Marca.
"The challenge at Malaga is no less than at Real Madrid or Villarreal," he added. "Challenges are personal."
Ferreira was appointed in June by new Malaga owner Sheikh Abdullah Bin Nasser Al-Thani, a member of the Qatari royal family, but nine matches into the new campaign the club have taken just seven points and are in the bottom three.
Malaga's next league match is at Espanyol on Saturday.
