The parade was delayed by heavy rain and lightning but tens of thousands of fans turned out
Blue flares were set off and fans threw inflatable bananas in the air as several of the players went shirtless in the heavy rain.
Manager Pep Guardiola was seen puffing on a cigar as fans climbed lamp-posts.
The parade was delayed by lightning storms. City beat Inter Milan 1-0 in the Champions League final.
It comes after the club clinched the Premier League and FA Cup this season.
Guardiola said his side's Champions League success following Rodri's 68-minute goal was "written in the stars".
Phil Foden shows off the Champions League trophy
A drenched Guardiola was later seen pumping his fists to the crowd as the players showed off all three trophies.
Defender Ruben Dias and striker Erling Haaland were among several players who went shirtless after they were drenched in the rain.
Haaland, 22, led the dancing players onto a stage just after 20:00 BST as midfielder Kalvin Phillips serenaded England defender John Stones.
Guardiola hailed the fans for coming out in the storms.
He said: "We had to be the best parade with this rain, otherwise it is not Manchester.
"We don't want sunshine, we want rain, so it was perfect. The fans are used to the rain."
Topless defender Ruben Dias held up the FA Cup in the rain
Captain Ilkay Gundogan said it was "incredible" that they had "three trophies".
England midfielder Jack Grealish said: "For the past 24 hours, I have had the best day and night.
"To be fair, I don't think I have slept."
The team had departed from Tonman Street, Deansgate, at the slightly delayed time of 19:00 BST due to stormy weather and travelled to St Mary's Gate.
The parade was delayed due to forecast lightning storms
One fan climbed up a set of traffic lights to get a good view of the parade
A Jack Grealish lookalike gets a good vantage point, too
The delays did not dampen the spirits of the fans.
Zoro and his family said they were looking forward to seeing Guardiola, Rodri, Bernardo Silva and Phil Foden.
City players show off the three trophies
He said: "This goes down in history for us. Pep has just redesigned the football world. It's a big statement but it's true."
The parade travelled through Cross Street and King Street, before finishing on the corner of Princess Street and Portland Street.
Zack, Nic and Noah have travelled from Blackpool to be at the parade
Zoro said Guardiola has "just redesigned the football world"
City became just the second English men's team to win the Treble, following in the footsteps of rivals Manchester United, who achieved the feat in 1999 under Sir Alex Ferguson.
The team were welcomed back by fans at Manchester Airport on Sunday after travelling from Istanbul, where the European final was played.
Manchester City clinched the Champions League after a 1-0 final win over Inter Milan
Crowds gather ahead of the open-top bus parade
A mural has been created on New Cathedral Street celebrating the team's success
A street vendor sold trophy balloons as fans waited for the parade
Former City boss Joe Royle said Guardiola's current side was one of the best teams English football had ever seen.
Royle, 74, who led the club from the third tier to the Premier League after back-to-back promotions in 1999 and 2000, said: "There's no doubt about it. They're one of, if not the best English club side there has been."
-- Courtesy of BBC Sport