It will be the relaunched team's first Tour after they took over Team Sky earlier this year.
"We believe it makes sense to go into the race with joint leaders as it gives us more options," Thomas, the first Welshman to win the race in 2018, said in a statement.
"Egan and I will work hard for each other and the team over the three weeks of the race... I can't wait to pull on the Team Ineos jersey for the first time in what is the biggest race of the year."
Thomas was given the all clear to defend his title despite crashing out of the Tour de Suisse this month, a few days after Froome needed surgery following an accident at the Criterium du Dauphine.
"It's no secret my build-up has been affected by the crash at Tour de Suisse, but I've had a good block of training since and I feel ready," Thomas added.
Bernal will go into his second Tour full of confidence after winning the Tour de Suisse last weekend.
"Last year's experience taught me a lot. As a rider, whatever you might think about the Tour from the outside you don't really know until you've raced it," the Colombian said.
"Now I know what to expect, I can be more relaxed about what lies ahead and even more focused on the racing."
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Christian Radnedge)
