The Manchester United star will lead out the Three Lions in the absence of regular skipper Steven Gerrard - who is suspended following his dismissal against Ukraine - and Frank Lampard, who was forced to withdraw from the squad with a thigh injury sustained in Chelsea's victory over Norwich on Saturday.
Speaking at the pre-match press conference, Rooney told reporters: "It’s a great honour, something I’m really proud of and it’s a big challenge for myself.
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Explaining the decision, Hodgson added: "I’m really pleased about that [to have Rooney available]. I enjoyed working with Wayne, we had a good Euros.
"I enjoyed working with him there. I’ve been a bit disappointed of course when he got that terrible gash.
"I was even worried at the time that it would keep him out not only of the September games but also the October games.
"Luckily he’s made a very quick recovery and now he’s available for the games and will certainly captain the team in the first one."
It is almost three years since Rooney last captained his country in a friendly against Brazil in Doha in November 2009 - a match they lost 1-0.
Rooney is yet to score for United this season but has been widely praised for his performances since returning from a gashed leg picked up against Fulham, laying on two goals in Sunday's 3-0 away win over Newcastle.