Brathwaite, who has captained West Indies seven times while standing in for Holder, will take the team into the two-Test series against Sri Lanka which begins on March 21.
"It is a huge honour to be given the captaincy of the West Indies Test team," he said. "I feel extremely proud and humbled that the board and selectors have given me the opportunity and responsibility to lead the team. The recent Test series win in Bangladesh was a fantastic achievement and I'm really looking forward to the upcoming home series against Sri Lanka, and I'm excited about what I believe this team can achieve in the future."
Roger Harper, the lead selector, said Brathwaite's role in the Bangladesh tour, where West Indies were without a number of first-choice players, had played a key part in making the change. They chased 395 to win the first Test, inspired by Kyle Mayers' debut double century, before clinching a 17-run victory in the second match.
"We all believe that Kraigg is the right man to lead our Test side at this point in time and I'm delighted that he has accepted the role," Harper said. "In the recent Test series against Bangladesh, Kraigg was able to motivate his players to play to a very high level and create the culture we are looking to establish where the team showed a collective determination to fight and a real hunger for success."
Holder, 29, who is among the game's leading allrounders with a Test batting average of 32.04 and a bowling return of 27.94, captained West Indies in 37 Tests since taking over in 2015 with 11 wins, five draws and 21 defeats.
"On behalf of CWI, I would like to thank Jason for all he has given to the game in the region while serving as Captain of our Test team," Jimmy Adams, CWI director of cricket, said. "Throughout his five-and-a-half-year tenure, he has led with dignity while always upholding the highest values of the sport. As the world's leading Test allrounder, we all believe that Jason still has a tremendous role to play in West Indies Test cricket for many years to come."
West Indies squad: Kraigg Brathwaite, Jermaine Blackwood, Nkrumah Bonner, Darren Bravo, John Campbell, Rahkeem Cornwall, Joshua Da Silva, Shannon Gabriel, Jason Holder, Alzarri Joseph, Kyle Mayers, Kemar Roach, Jomel Warrican