Greipel was in the company of sprinters Mark Cavendish, Alexander Kristoff and Peter Sagan as they entered the Champs Elysees in Paris. Kristoff took the early lead, but Greipel edged past him to earn his fourth stage win of Le Tour.
Froome and his Team Sky teammates crossed the line behind the peloton arm-in-arm in a great display of camaraderie.
The Kenyan-born rider earned his second win of the Tour de France, following on from his win in 2013.
Race organisers neutralised the riders' times for the overall general classification with 70km to go due to the wet weather and very slippery conditions.
Froome finished 1:12 ahead of Nairo Quintana in the overall GC, while Quintana's Movistar teammate and fellow Colombian Alejandro Valverde would settle for third place on the podium, 5:25 off the pace.
Le Tour was disappointing for seven-time Grand Tour winner Alberto Contador, as the Spaniard would only manage fifth place behind defending champion Vincenzo Nibali. The duo were eight and nine minutes behind Froome in the GC.
Quintana won the white jersey for the best young rider, while Sagan won the points classification and the green jersey.
Stage 21 result:
1 Andre Greipel (Ger) Lotto Soudal 02:49:41
2 Bryan Coquard (Fra) Team Europcar
3 Alexander Kristoff (Nor) Team Katusha
4 Edvald Boasson Hagen (Nor) MTN – Qhubeka
5 Arnaud Demare (Fra) FDJ.fr
6 Mark Cavendish (GBr) Etixx – Quick-Step
7 Peter Sagan (Svk) Tinkoff-Saxo
8 John Degenkolb (Ger) Team Giant-Alpecin
9 Michael Matthews (Aus) Orica GreenEdge
10 Ramunas Navardauskas (Ltu) Cannondale-Garmin Pro Cycling Team
Final overall general classification:
1 Christopher Froome (GBr) Team Sky 83:19:15
2 Nairo Quintana (Col) Movistar Team 00:01:12
3 Alejandro Valverde (Spa) Movistar Team 00:05:25
4 Vincenzo Nibali (Ita) Astana Pro Team 00:08:36
5 Alberto Contador (Spa) Tinkoff-Saxo 00:09:48
6 Robert Gesink (Ned) Team LottoNL-Jumbo 00:10:47
7 Bauke Mollema (Ned) Trek Factory Racing 00:15:14
8 Mathias Frank (Swi) IAM Cycling 00:15:39
9 Romain Bardet (Fra) AG2R La Mondiale 00:16:00
10 Pierre Rolland (Fra) Team Europcar 00:17:30