The PSG board accepted Alain Cayzac's resignation Monday and named Tahar, a lawyer, to replace him, the club said in a statement. Cayzac had presided over the club for almost two years.
Tahar had headed the PSG Association and was PSG's lawyer from 1978-91, according to the sports daily L'Equipe.
Press reports had said that Tahar would likely be named to succeed Cayzac, but only as interim president.
PSG is in 18th place in the French league and is three points away from safety with only four matches remaining.
Crisis talks were held last weekend with Sebastien Bazin, a representative of the club shareholders Colony Capital, and PSG coach Paul Le Guen.
The club has hired Michel Moulin as director of sport to work alongside Le Guen, whose position will be further weakened if PSG loses its next big challenge - a home game Saturday against Auxerre.
A news conference by Moulin set for Wednesday evening was abruptly cancelled.
Security will be intensified this week after PSG fans vandalised the club's training ground in the early hours of Sunday morning.
Slogans attacking Le Guen were sprayed on walls and PSG defender Sylvain Armand's Porsche was damaged.
PSG has a long-standing problem with a hardcore hooligan element, and last week French Interior Minister Michelle Alliot-Marie ordered that a group of PSG fans - known as the "Boulogne Boys" - be disbanded.