Leading 2-1 from the first leg of the last 16 tie, PSG stretched their lead when Ibrahimovic crossed for Adrien Rabiot to tap in and although Diego Costa's slick finish gave Chelsea hope, Ibrahimovic volleyed home in the 67th minute to complete a 4-2 aggregate success.
Victory took Laurent Blanc's PSG into the quarter-finals for the fourth year in a row, while Chelsea were left to contemplate a first season without Champions League football since 2002-03.
Ten points off the top four in the Premier League, Chelsea's hopes of qualifying for the Champions League via the league are paper-thin and their chances of bouncing back in Saturday's FA Cup quarter-final at Everton were jeopardised by injuries to Costa and Eden Hazard.
Much of the pre-game attention had focused on Costa and Ibrahimovic, and it was PSG's Swedish talisman who emerged triumphant as the French champions claimed further revenge for their elimination by Chelsea in 2014.
Sent off at Stamford Bridge a year ago, when PSG's 2-2 draw took them through on away goals, he belied doubts about his big-game temperament to keep the runaway Ligue 1 leaders on course for a potential quadruple.
Marco Verratti's failure to recover from a groin injury meant that Rabiot started in midfield for PSG and he almost cost his side an early goal with a loose pass that culminated in Kevin Trapp parrying from Costa.
But with Angel di Maria and Lucas Moura abandoning their wings at will, PSG's attack bristled with menace and in the sixth minute stand-in Chelsea captain Branislav Ivanovic had to slide a shot from Di Maria off the line after he had been played in by Lucas.
Ten minutes later PSG tightened their grip on the tie as Di Maria played a pass behind the Chelsea defence for Ibrahimovic, whose masterful low cross was turned in by Rabiot.
Leading 3-1 on aggregate, it should have been the cue for PSG to take the sting out of the game, but instead they allowed Chelsea to level on the night with a goal that owed equally to Thiago Motta's carelessness in possession and the hosts' dazzling interplay.
After Pedro Rodriguez nipped in to rob Motta, Willian played a quick one-two with the Spaniard before feeding Costa, who expertly turned Thiago Silva and drilled home left-footed.
Ibrahimovic put a header straight at Thibaut Courtois from a Lucas cross, but the hosts finished the half with the wind in their sails, Cesc Fabregas, Hazard and Costa all going close to levelling the tie.
Costa had another sight of goal early in the second half, David Luiz blocking his shot from Willian's cut-back, but the Spain international, who had been a constant menace, had to go off on the hour after appearing to hurt his calf, with Bertrand Traore replacing him.
Guus Hiddink's side came close to making light of Costa's departure, but Trapp produced a sharp double-save to thwart Willian and then Hazard, and within two minutes the tie was over.
Motta's astute pass to the left found Di Maria in acres of space and his fine cross was volleyed in emphatically by Ibrahimovic.
Chelsea's mood darkened yet further with 14 minutes remaining when Hazard limped off, but the hosts' fire had already burnt itself out.