"To be named as England captain is a dream come true for me personally and, of course, for my family," Rooney, who has scored 40 goals in 95 international appearances, said in a statement.
"It is something I will take massive pride in doing.
"As a kid I always loved the occasion of watching a big England game on the television," the 28-year-old added. "Back then I had a burning ambition to play for my country. Now to be appointed captain is beyond my wildest dreams."
Coach Roy Hodgson made the announcement at a media conference at Wembley as he unveiled his squad for the fixtures against Norway and Switzerland.
"I gave it a lot of thought but Wayne is an obvious choice," Hodgson told reporters.
"He deserves it - his commitment to the cause, his experience. He has captained England in the past and, of course, he has that responsibility at Manchester United now.
"I've had a long conversation with him and he's prepared to accept the pressures that the England captaincy brings. It's important that the player wants to take on that enormous responsibility."
Hodgson, under pressure as England coach for the first time after his team's poor performance at the World Cup, said he believed Rooney was well suited to the role despite lingering question marks over the player's maturity and temperament.
Rooney, who has had on-field disciplinary problems in his career, was sent off playing for England against Portugal at the 2006 World Cup and against Montenegro in a Euro 2012 qualifier.
He was also heavily criticized after mouthing the words "nice to see your home fans boo you" following England's dismal 0-0 draw with Algeria at the 2010 World Cup.
But Hodgson said: "I've got to judge him on the two years I've been with him.
"It's not for me to look back too much and whatever misdemeanors the player may have had. In the two years with me I've had no reason whatsoever to question anything about his character or desire to play for his country or his wholehearted willingness to offer himself in every situation.
"I'm not concerned about anything else, but he has that baggage with him and he will have to accept that as an added part of the pressure."
Hodgson said he would "shy away" from the theory that the captaincy would bring more out of Rooney as a player. But he added: "With his 95 caps, goals and all the things he has done, what we've seen is his willingness to take responsibility. All I can hope is that he continues to play well and shoulders the responsibility as well as the captains before him.
"When you name a captain it does go through your head that it will make it a lot harder if I had to drop him.
"I don't think Wayne would expect me to keep him in the team just because he is captain. I'd like to think if it was necessary I would do (drop him) and I'm pretty convinced he would accept it.
"We've got players like Joe Hart and Gary Cahill, in that they are experienced players... and play for big clubs. It would be harsh on them to say Wayne was the only choice. But had I chosen them, it would have been unfair on Wayne Rooney - for most people it was his time and moment."
Rooney, born in Croxteth in Liverpool, said he would talk about the role with Gerrard, the midfielder who retired from international soccer after England's disappointing World Cup in Brazil.
"I have played under some fantastic captains at both Manchester United and England and would hope that I have picked up some of their strongest qualities," Rooney said.
"I intend to speak with Steven about different aspects of the role. We had a great relationship from the moment we played together for our country right up to our final game in Brazil. I am sure if I ever need to seek his advice he will be there to help."
He added: "I hope I will have the full backing of the fans. I am their type of player once I am on that pitch. My only thought is to win and give everything I have got. Sharing that desire will be the way I want to captain the team."
Rooney became the then youngest player to play for England when he made his debut against Australia in a friendly in 2003 aged 17 and 111 days.
He has captained England on two previous occasions, and played in five major tournaments, but, like every player of his generation, has not tasted significant success in an England shirt.
His first goal at a World Cup finals did not arrive until this year, when he scored in England's 2-1 defeat by Uruguay in the group stage.
He is, however, on course to break Bobby Charlton's all-time goalscoring record of 49 England goals. Rooney is currently fourth on the list, behind Charlton, Gary Lineker (48) and Jimmy Greaves (44).
(Writing by Stephen Wood, editing by Pritha Sarkar)