With Gerrard suspended, the 26-year-old striker captained Hodgson's side for the first time during the 5-0 victory over San Marino in a World Cup 2014 qualifying match at Wembley on Friday night, scoring twice in the process.
And national boss Hodgson stated it was always his plan for Rooney to captain the side once Gerrard steps down, despite the return of the experienced Chelsea midfielder Frank Lampard to the squad.
Asked by reporters whether Rooney would be the future captain, Hodgson replied: "Yes. It's something he's very proud of and something he wants to do. He does take playing for England unbelievably seriously and that's a good thing for us.
"Wayne [Rooney] was my vice-captain in the Euros  – at least he was from the moment he could start playing again.
"Steve [Gerrard] was given the captain's armband and I made it clear Wayne would be the vice-captain."Frank [Lampard] has come back in and captained the team, but I always had it in my mind that Wayne would be vice-captain."
Steven Gerrard will return to the fold to captain England against Poland on Tuesday evening, but Rooney can't wait to take on the role full-time after getting a taste of the responsibility of leading his country.
"Of course I dream of captaining England to glory one day", he said.
"As a young player, your dream is to play for England and, once you play, the next step is to captain your country.
"I've done it now. It was a great honour and hopefully one day it can be full-time."