The British rider, who came into the stage tied on 34 stage wins with Merckx was beaten to the line by Wout van Aert and Jasper Philipsen in Paris. However, Cavendish's third place was enough to secure his second green jersey.
Merckx's record has stood since 1975, when he won a split stage time trial in Auch to make it 35 stage wins at the race.
Cavendish looked on the bright side after the finish, however. "I’m very happy. One month ago I wasn’t supposed to do the Tour de France and now I am here, after three weeks that will live long in memory," he said in a team press release.
"I never imagined I would be again wearing green on the Champs-Élysées, but here I am, thanks to the amazing riders and staff of Deceuninck-Quickstep. They were a big part of this success and together we’ve been through so many emotions.”
Cavendish's remarkable comeback still included four stage wins in this year's race - a huge achievement for a rider who almost looked set to retire at the end of 2020.
At that point, he was without a contract and had no Tour de France stage wins since 2016 but a last-minute contract offer came his way from Patrick Lefevere with a one-year deal put on the table from Deceuninck-QuickStep.
Since joining the team, the British sprinter won four stages in the Tour of Turkey, backing that race up with a stage win in the Tour of Belgium. However, he only received a late call-up for this year's Tour de France after reigning green jersey Sam Bennett was ruled out through injury.
Bennett was due to lead the team in the sprints and was even put in the line-up with just a week to go. However, the Irishman was dropped with just days to spare. That opened up the door for Cavendish, who hadn't won a stage in the race since 2016. He had not even raced the Tour since 2018 when he finished over the time limit on stage 11.
However, at this year's edition, he found his best form and made use of the strongest leadout in the entire race. His first win in this year's race came on stage 4 to Fougères, which he followed up two days later with victory on stage 6 to Châteauroux. Further wins came in Valence and Carcassonne on stages 10 and 13.
Cavendish sealed the green jersey with 337 points with Michael Matthews (Team BikeExchange) in second on 291 points. Sonny Colbrelli (Bahrain Victorious) was third on 227 points.
"For me, to be back at this race that I love so much and do what I did was a dream," Cavendish said. "I am incredibly happy that I have my family here, as I haven’t seen them in the last five weeks and it feels great to share with all of them these unforgettable moments."
Watch the sprint finish
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