Cook has been under pressure due to a poor run of form with the bat but he scored his first test century for nearly two years in the recent drawn series in West Indies.
"Alastair Cook is the right man to lead the England team," Strauss told reporters at Lord's on Tuesday.
"It has been a difficult 18 months but it was great to see him come back to form in the West Indies."
The decision to name the 24-year-old Root as vice-captain in place of Ian Bell suggested Strauss is already planning a long-term strategy for the development of the team.
"It was time to bring Joe into a leadership role," Strauss said. "I hear he is a strong voice in the dressing-room. It is a strategic decision."
Strauss also hinted that there would be more differentiation between the test and one-day teams, confirming that Eoin Morgan would continue as captain of the limited-overs side.
"We need more separation between the test and one-day teams and Eoin has my full support," Strauss said.
"I will be looking at ways in which we can rest players and
support staff so we can achieve maximum success on the pitch."
Strauss also revealed that batsman Kevin Pietersen, sacked last year and still not part of England's plans on the field despite scoring 355 not out for Surrey, had been offered a consultancy role with the one-day side.
"Kevin rejected the offer," Strauss said. "He was not happy with the decision not to recall him to the side and I did not expect him to be."
Strauss also explained his decision to fire Peter Moores as coach.
"I felt it was important to change the coach," Strauss said. "In some areas of strategy and tactics he (Moores) was exposed.
"The England coach's job is a very powerful position in world cricket and we need a guy who has the energy and vision to take the team forward."
Strauss, who captained England to two Ashes triumphs, tried to sound a positive note despite all the recent criticism of the team.
"It is an exciting time," he said. "We should not forget that the last decade has been one of the most successful in England's history but the game is evolving very quickly.
"I have to implement a team culture which is fundamental to any success and we have to find self-reliant cricketers who can make the right decisions where it matters most out on the field."
(Editing by Toby Davis)
Share
