Sir Bradley Wiggins won the race for a second time in 2012 before going on to become the first British victor of the Tour, while Froome has won it on four occasions, each time going on to claim the yellow jersey in Paris.
"It's incredible, it hasn't sunk in yet!" said Thomas, who joins some illustrious company and must now be considered a contender for overall Tour de France success.
"Throughout the race I was never thinking about the end result, it was always about the next day or the next climb". It's a massive race and it's an incredible feeling.
He follows in the footsteps of compatriots Bradley Wiggins, who won the race twice, and three-time victor Chris Froome. France's Romain Bardet, of AG2R, jumped to third from seventh overnight and is at 2min 01sec.
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Yates, of Mitchelton-Scott, pulled clear of Spanish rider Dani Navarro 50m from the line at the finish to the 136km closing day's ride to the ski resort of Le Bettex.
Yates said: "The Tour de France has been my main goal for the whole season".
"From the start of the year I said I wanted to get there [the Tour de France] in the best shape possible and I'm on course for that".
But the Frenchman ran out of gas as Thomas quickly narrowed the gap on Martin, who stood up out of the saddle in a final show of defiance. Geraint Thomas (GBR) Team Sky 24:43:12 2. Romain Bardet (FRA/ALM) 2:01, 4. Emanuel Buchmann (GER/BOR) 14, 5. Geraint Thomas (GBR/SKY) at 21sec, 3. Guillaume Martin (FRA) Wanty - Groupe Gobert +28 9.
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