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.
"Throughout the race I was never thinking about the end result, it was always about the next day or the next climb".
Team Sky's Thomas came home 21 seconds behind Spain's Bilbao, who staged a heroic solo effort 12 kilometres from the finish to triumph for Astana.
"It's incredible. I didn't let myself think so far ahead".
And Yates' second place ensured the first ever British one-two in the race, with his second win on the WorldTour in 2018 confirming both he and the Welshman will head to the Tour de France in top form. Froome has won the Dauphine before each of his four Tour victories.
"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". Cycling's governing body, the UCI, are still investigating with Froome denying any wrongdoing.
"It's been a learning process starting in a new team so getting this win for UAE is great", he said.
"Ive been feeling good all year", the Irishman said after the race.
He added: "The guys were just incredible, They rode really well for me". We're getting closer and closer so I'm happy to get confidence from this race.
Having been the last man standing in support of Thomas, meanwhile, Tao Geoghegan Hart climbed to 13th overall to follow his fifth place in support of Egan Arley Bernal's Amgen Tour of California win last month.