The Astana rider completed the route, which started in Frontenex, in a time of 3:34:11.
Thomas finished fifth on the final day in the end, having moved into the yellow jersey and clear of his rivals thanks to second place finishes at Valmorel and La Rosiere on stages five and six.
The two-time Olympic champion, who also has a win at Paris-Nice on his palmares, was joined on the podium by Bury's Adam Yates (Mitchelton-Scott), who secured second place overall by winning the final stage of the race.
"I was counting down the kilometres on the last climb and knew I had about 1'20" to lose to Adam Yates so, as each kilometre went by, I was more confident and happy. Now I realise I've won a massive race. I can rest a little bit and wait for July.
It came on a 110 kilometres stage from Frontenex which is nearly a carbon copy of this year's Tour de France stage 11.
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"It's been two back-to-back hard stages", he added.
"It's not a great situation for him, the team or just cycling in general", Thomas said.
But it did give Thomas the chance to lead Team Sky.
Thomas then launched a spectacular bid to catch Martin and only French hope Romain Bardet was able to follow.
Team Sky's Thomas suffered two punctures during the 136km stage from Moutiers to Saint-Gervais Mont Blanc, but took a wheel from a teammate on the second occasion and was paced back to the peloton by Michal Kwiatkowski and Dylan van Baarle. Pierre Rolland (FRA) Team EF Education First - +41 Drapac p/b Cannondale Overall leaders 1.