The England and Wales Cricket Board (ECB), on Monday, announced 26-year-old Root as the new skipper for the longer format. He is the 80th Test leader of England. All-rounder Ben Stokes will be his deputy.
"It is a huge honour to be given the England Test captaincy," said Root.
"I feel privileged, humbled and very excited. We have a very good group of players and I'm looking forward to leading them out in the summer, building on Alastair's achievements and making the most of our talents in the years ahead.
"The senior guys in the changing room play a very influential role and whilst there's a natural progression for me it's a huge support to know that they are there to help and advise," he added.
Colin Graves, Chairman of the ECB, approved the appointments on Sunday evening (February 12) following the recommendation of the selectors under the guidance of Director of England Cricket Andrew Strauss, a former skipper.
"Joe Root is the perfect choice for England Test captain. I'm delighted that he has accepted the role and will now help to take the team to the next level," Graves said.
Root made his Test debut in December 2012 and was named vice-captain to Cook in 2015. He scored the first of his 11 Test centuries at Headingley in May 2013 and currently has a total of 4,594 Test runs from 53 Tests at an average of 52.80, placing him third in the ICC rankings for Test batsmen.