J.P. Morgan's Dimon told CNBC earlier in June that this is a long-term initiative. He said there are a lot of ideas out there and things they know can be done better, pointing to fraud, administrative costs, overuse and underuse of various drugs, and specialized procedures.
Gawande has been vocal about his ideas to improve health care and lower costs. He has advocated more integration in health care, saying in a 2012 TED Talk that the ones getting the best results at the lowest costs have found ways to get all the different pieces to come together into a whole.
"There's a famous thought experiment that touches exactly on this that said, what if you built a car from the very best car parts? Well it would lead you to put in Porsche brakes, a Ferrari engine, a Volvo body, a BMW chassis. And you put it all together and what do you get? A very expensive pile of junk that does not go anywhere. And that is what medicine can feel like sometimes. It's not a system," he said.
Despite momentum around the venture, some health-care experts have been skeptical about whether Buffett, Dimon and Bezos, while business icons, can simplify the current system.
Andy Slavitt, who was chief of the Centers for Medicare and Medicaid Services during the Obama administration, is among the consultants the trio spoke with. He praised the decision to have Gawande lead the effort.
"There are few better people in health care than [Gawande]," he said. "They are fortunate to have him, principally because of his moral leadership."
Buffett said in a statement that the trio was looking for "talent and dedication" when interviewing candidates.
"We said at the outset that the degree of difficulty is high and success is going to require an expert's knowledge, a beginner's mind, and a long-term orientation," Bezos said in a statement. "[Gawande] embodies all three, and we're starting strong as we move forward in this challenging and worthwhile endeavor."
— CNBC's Bertha Coombs contributed to this report.