The Barbadian all-rounder has made 21 ODI appearances, taking 29 wickets and scoring 109 runs, has captained the West Indies A team.
Bravo only replaced Darren Sammy as skipper last year, but his tenure has proved to be a short one after it was announced on Saturday that Holder will take over the role.
Chairman of the selectors Clive Lloyd is backing 23-year-old Holder to be a success as skipper.
He said: "Jason is one of the good, young players who we believe will form part of the long-term future of West Indies Cricket. We expect him to be around for a very long time.
"He is a young man with a very bright future. We have invested in him.
"He was part of High Performance Centre and he also played for the West Indies Under-19 Team and the West Indies 'A' Team.
"We know he will continue to grow and demonstrate leadership. He has a very good cricketing brain and has the makings of a very good leader.
"Some might say it's close to the time of next year's ICC Cricket World Cup in Australia and New Zealand but we know that we have a good One-Day team which can do very well."
Holder will lead his country for the first time in a five-match series in South Africa next month.