Froome finished the race four minutes and five seconds ahead of Frenchman Romain Bardet (Ag2r La Mondiale), with Nairo Quintana (Movistar) in third at 4-21.
Along with Froome's overall win and two stage wins, plus four stage wins for Mark Cavendish (Dimension Data) and one for Steve Cummings (Dimension Data), British success continued with Adam Yates (Orica-BikeExchange) securing the white jersey of best young rider and placing fourth overall. It's the first time a British rider has ever topped the best young rider classification and has now set him up as an exciting new Grand Tour prospect.
German sprinter André Greipel (Lotto-Soudal) won the bunch sprint at the end of the final stage, out-pacing points classification winner Peter Sagan (Tinkoff) to the line. Alexander Kristoff (Katusha) was third. British sprinter Dan McLay was 12th, having completed his first Tour.
It's Greipel's sole stage victory in the 2016 race, and is his 11th Grand Tour since 2008 with at least one stage victory.
Before the frantic finale, the traditional procession after the start of the last stage saw a slow pace as riders chatted and got to enjoy rolling along in the warm, sunny weather. Froome and Sky team-mates indulged in an unconventional bottle of beer followed by a more conventional glass of Champagne.
It wasn't until the race hit the Champs Élysées that the pace picked up and a break formed with 50km to go.
Jan Barta (Bora), Marcus Burghardt (BMC), Rui Costa (Lampre-Merida), Lawson Craddock (Cannondale-Drapac), Brice Feillu (Fortuneo-Vital Concept), Alexis Gougeard (Ag2r-La Mondiale), Jérémy Roy (FDJ) and Daniel Teklehaimanot (Dimension Data) were the eight riders to finally get away.
Marcel Kittel (Etixx-QuickStep) suffered a technical mishap, and was seen throwing his rear wheel across the road after a couple of bike changes. He then paced himself back up to the bunch without the help of team-mates, but the effort would see him out of the running in the final sprint.
The break was joined by Sky duo Luke Rowe and Wout Poels, who bridged over with 18km to go evidently trying to get rid of any unexpended energy from the previous three weeks.
All escapees were caught with 10km to go, and the bunch was still all together with one lap of the cobbled loop and 6.6km to go. It took a while for the sprinters' teams to get organised at the front, with a jumble of riders initially jostling for position.
A couple of late crashes took out a few riders, and French sprinter Bryan Coquard (Direct Energie) appeared to suffer from a puncture with 3km to go, his hope of a stage win over.
The tight corners into the finish straight disrupted Greipel's Lotto-Soudal sprint train, but he jumped on Kristoff's rear wheel and accelerated away on the cobbles. Sagan was gaining on him as Kristoff faded, but Greipel lunged clear on the line to win on the Champs Élysées for a second consecutive year.
Tony Martin (Etixx-QuickStep) was a surprise abandon during the final stage after suffering from knee pain during the stage. It left 174 riders left in the race, the highest ever number of finishers in the race's 103 editions – the previous record was 170 in 2010.
Tour de France 2016, stage 21: Chantilly to Paris Champs-Élysées, 113km
1. André Greipel (Ger) Lotto-Soudal in 2-43-08
2. Peter Sagan (Svk) Tinkoff
3. Alexander Kristoff (Nor) Katusha
4. Edvald Boasson Hagen (Nor) Dimension Data
5. Michael Matthews (Aus) Orica-BikeExchange
6. Jasper Stuyven (Bel) Trek-Segafredo
7. Ramunas Navardauskas (Ltu) Cannondale-Drapac
8. Christophe Laporte (Fra) Cofidis
9. Sam Bennett (Irl) Bora-Argon 18
10. Janse Van Rensburg (RSA) Dimension Data all same time
Final general classification
1. Chris Froome (GBr) Team Sky in 89-06-01
2. Romain Bardet (Fra) Ag2r La Mondiale, at 4-05
3. Nairo Quintana (Col) Movistar at 4-21
4. Adam Yates (GBr) Orica-BikeExchange at 4-42
5. Richie Porte (Aus) BMC at 5-17
6. Alejandro Valverde (Esp) Movistar at 6-16
7. Joaquim Rodriguez (Esp) Katusha at 6-58
8. Louis Meintjes (RSA) Lampre-Merida at 6-58
9. Dan Martin (Irl) Etixx-Quick Step at 7-04
10. Roman Kreuziger (Cze) Tinkoff at 7-11
King of the Mountains classification: Rafal Majka (Pol) Tinkoff
Points classification: Peter Sagan (Svk) Tinkoff
Young rider classification: Adam Yates (GBr) Orica-BikeExchange
Best team: Movistar
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