Video report by ITV News Correspondent Geraint Vincent
An estimated 750,000 people lined the streets of Liverpool to welcome back the Champions League winners, Liverpool City Council said.
The Reds 2-0 victory over Tottenham in Madrid sparked jubilant scenes on Saturday night, with fans celebrating into the early hours.
Jurgen Klopp and his team arrived at Liverpool John Lennon Airport on Sunday, before boarding an open-top bus emblazoned with the message "Champions of Europe".
The smiling team, holding aloft their sixth European Cup, were met by a sea of red as they embarked on a tour of the city centre.
Huge crowds of Liverpool fans wearing shirts and flying flags packed out roadsides, chanting and singing the team’s praises in the sunshine.
The parade comes just hours after the team touched down at Liverpool's John Lennon Airport.
Hours ahead of the parade starting, fans had already begun to line the route, eager to catch a glimpse of the team and the trophy.
Parents with their children told how they were there to make memories, while others simply wanted to soak up the atmosphere and enjoy being part of the Liverpool "family".
Although many fans were Liverpool born and bred, some had come from as far away as Vancouver in Canada to take part in the celebrations.
The Reds lifted their sixth title in Europe’s premier competition after beating Tottenham by two goals in the final on Saturday night.
Celebrations continued well into the night both in Madrid and around Liverpool, with many meeting outside Anfield with flags and scarves.
After setting off from Allerton Maze, south Liverpool, the bus travelled northbound on Queens Drive towards the Fiveways roundabout and Rocket flyover.
From there it journeyed along Queens Drive, Mill Bank, West Derby Road, Islington, Leeds Street and The Strand before finishing at Blundell Street, along the city’s UNESCO World Heritage waterfront.
Ahead of the parade, Mayor of Liverpool Joe Anderson tweeted: “Make sure you get to your vantage points around the City on time to welcome home the victorious @LFC the Liverpool team bus parade route is below and starts at 4.00 pm. Have great day and well done Liverpool FC.”
The team's victory sparked rapturous scenes in Liverpool on Saturday night with red smoke filling the air from flares.
A huge party broke out as thousands of fans left pub TV screens to dance and sing in the streets.
On Matthew Street, strewn with beer glasses and bottles, Ged Evans, 34, from Wrexham, said: "This is the greatest night of my life, short of my kids being born.
"If you can't be in Madrid then there's nowhere else on Earth to be tonight than inLiverpool."
Many Liverpool fans had gone to great lengths to travel to the Spanish capital itself and watch the game, many without having tickets.
Travelling supporters who failed to get into the match followed the game on mobile phones outside the stadium.
Scores of others were turned away amid claims some fans had paid thousands on the black market for tickets which turned out to be fakes.
But pre-game concerns over potential strains between fans and police, the lack of tickets for travelling supporters and the absence of any giant screens were put to one side following Liverpool's victory.
Tens of thousands of jubilant fans poured into Madrid's plazas to celebrate the Reds' latest Champions League title with cans of lager.
The parade takes place at a time when Liverpool is already staging two major events – River Festival Liverpool and the Bordeaux Wine Festival – which are already expected to attract tens of thousands of people to the city.