Brindisi, who steered Independiente to a league title in 1994, will be presented officially to the media as the team's new coach later, media reported.
The 62-year-old, a former Las Palmas, Boca Juniors and Argentina 1974 World Cup midfielder, replaces Americo Gallego who resigned at the weekend, and is set to sign until the end of next season.
Brindisi refused the club's initial offer on Monday but Independiente president Javier Cantero persuaded him to take the hot potato at a meeting that ended after midnight.
Cantero was helped by Argentine Football Association president Julio Grondona, an Independiente fan and former club chairman, who also spoke to Brindisi about "helping them out", reports said.
The Red Devils, along with Boca the only teams never to have been relegated in Argentina, are in the bottom three of the parallel relegation standings based on team's average points over three seasons.
Independiente have managed just two wins and nine points from nine matches in the "Final" championship and only 26 from 28 including the "Inicial" in the first half of the season.
Supporters threatened players last week and again on Friday night after they were held 1-1 at home by Union, direct rivals in the battle to avoid relegation to the second-tier Primera B Nacional where big rivals River Plate spent the 2011/12 season.
Brindisi was reported as wanting former Barcelona and Argentina centre back Gabriel Milito, who began and ended his playing career at Independiente, as his right-hand man.
Independiente's next match on Saturday is away to Atletico Rafaela, who are coached by former midfielder Jorge Burruchaga, a member of the team that won their seventh Libertadores Cup and the club world title in 1984.
- Sports & Recreation