The German had been pushed into the runner-up spot in each of the opening two stages, but launched a timely assault to seize the leader’s jersey as the stage finished on the Magny-Cours race track.
Matt Goss and Jose Joaquin Rojas finished second and third respectively.
"That was unbelievable, everything worked out perfectly today," said Degenkolb. "We tried twice already on the first two stages but each time it didn't quite work out, but today it was spot on.
"I'm really happy that I can finally thank my teammates with this win after giving me complete support over the past few days."
Three Frenchman – Perrig Quemeneur, Julien Fouchard and Romain Feillu – broke clear of the pack early on and established a three minute advantage.
But the peloton slowly reeled in the trio, with Quemeneur eventually electing to make a solo break for glory when the gap shrunk to less than a minute.
Quemeneur was overhauled two kilometres from the finish as the sprinters primed themselves for an attack, and it was Degenkolb’s Giant-Shimano team who grabbed victory to make amends for the for their near-misses of the two previous stages.
Stage three results
1. John Degenkolb (Germany / Giant) 4:27:26"
2. Matthew Goss (Australia / Orica) ST
3. Jose Joaquin Rojas (Spain / Movistar)
4. Borut Bozic (Slovenia / Astana)
5. Tom Boonen (Belgium / Omega Pharma - Quick-Step)
6. Alexander Kristoff (Norway / Katusha)
7. Nacer Bouhanni (France / FDJ.fr)
8. Thor Hushovd (Norway / BMC Racing)
9. Gert Steegmans (Belgium / Omega Pharma - Quick-Step)
10. Moreno Hofland (Netherlands / Belkin)
1. John Degenkolb (Germany / Giant) 13:14:01"
2. Nacer Bouhanni (France / FDJ.fr) +8"
3. Moreno Hofland (Netherlands / Belkin) +12"
4. Jose Joaquin Rojas (Spain / Movistar) +18"
5. Geraint Thomas (Britain / Team Sky) +21"
6. Bryan Coquard (France / Europcar) +22"
7. Alexander Kristoff (Norway / Katusha)
8. Nikolai Trussov (Russia / Tinkoff - Saxo)
9. Samuel Dumoulin (France / AG2R)
10. Marco Marcato (Italy / Cannondale)
- Sports & Recreation
- Jose Joaquin Rojas
- Perrig Quemeneur
- Matt Goss