Both sides have suffered disappointing exits from the competition in recent seasons and City came into this clash with a big advantage having come from behind to win 2-1 in Paris in the first leg.
"What we have done the last four years has been incredible," City manager Pep Guardiola said. "The Champions League is the hardest and getting to the final was the hardest thing for us to achieve.
"We deserve to be there for everything we have done at the club in the past four or five years.
"I want to thank the former players who helped take us to another level -- Joe Hart, Vincent Kompany and David Silva. This is because of them, they helped take us to another level.
Without Kylian Mbappe, was so important in wins away at Barcelona and Bayern Munich in previous rounds, benched due to a calf injury which kept him out of Saturday's 2-1 win over Lens, PSG lacked that killer touch in attack.
"That [Mbappe's absence] cannot be an excuse, we are a team," PSG manager Mauricio Pochettino said. "Of course, it's unlucky he was not ready to help the team, but that's not an excuse.
"We cannot use that excuse because the performance from the team was good."
But they started brightly despite the difficult conditions of a snowy Manchester, and thought they had been presented with an opportunity for the perfect start when referee Bjorn Kuipers awarded the visitors a penalty for an alleged handball by Oleksandr Zinchenko but, after a VAR review and a look at the monitor, the Dutch referee overturned his initial decision.
The decision galvanised City who took the lead thanks to the superb vision of goalkeeper Ederson whose kick upfield found Zinchenko in the PSG half. The Ukraine international pulled it back for Kevin De Bruyne, whose shot was blocked by Marquinhos and Mahrez picked up the loose ball and drilled it past goalkeeper Keylor Navas.
PSG failed to create too many clear cut chances with Angel Di Maria firing wide after capitalising on a mix up in the City defence and Marquinhos hit the bar with a close-range header.
Like in the first leg when, on that occasion they were trailing 1-0, City stepped things up in the second half and Phil Foden twice came close to scoring a second before Mahrez scored a brilliant second on 63 minutes following some brilliant combination play between Foden and De Bruyne.
PSG's frustration and their inability to compete with City was evident again as Di Maria was sent off for a petulant kick out at City's Fernandinho on 69 minutes. Teammate Idrissa Gueye was absent for this clash for a red card in the first leg.
"We played with character. We have to believe in ourselves, we will succeed," said PSG midfielder Marco Verratti.
"Against top quality players you need to put in a shift. We managed it well considering the talent they have. It is a team game. We all celebrate a goal. For us as defenders it is keeping clean sheets. We have done tremendously well with that this season. Blocking a shot is like scoring a goal for me," City defender Kyle Walker said.
City could now win a treble, having already clinched the EFL Cup and are just a point away from being crowned Premier League champions. For boss Pep Guardiola, this will be his first Champions League final since his second victory with Barcelona in 2011.