Manchester United striker Wayne Rooney takes a free kick during the pre-season friendly match between Manchester United and Valencia at Old Trafford in Manchester on August 12, 2014Manchester United striker Wayne Rooney takes a free kick during the pre-season friendly match between Manchester United and Valencia at Old Trafford in Manchester on August 12, 2014 (AFP Photo/Paul Ellis)
The 28-year-old forward has won 95 caps since making his debut against Australia in February 2003, scoring 40 goals, and was also named captain of United two weeks ago.
He succeeds Liverpool midfielder Gerrard, who stepped down after England's group-phase exit at the World Cup, and will begin his tenure as permanent captain in next week's friendly at home to Norway.
"I think Wayne's an obvious choice and he certainly deserves it," Hodgson told journalists.
"His commitment to the cause, his experience, the fact he's already captained England in the past, and now he has the responsibility at Manchester United -- all these factors weighed on my thought process.
"I had a long conversation with him and he's prepared to accept the pressures that the England captaincy brings, because it's quite important to make sure the person to whom you're offering the captaincy is ready to take on that responsibility."
In a statement published on the Football Association website, Rooney said: "To be named as England captain is a dream come true for me personally and of course my family. It is something that I will take massive pride in doing.
"As a kid I always loved watching a big England game on the television. Back then I had a burning ambition to play for my country. To be appointed captain is beyond my wildest dreams.
"I would obviously like to thank Roy and the coaching staff for having the belief and confidence in me to do the job."
- Four new faces -
Hodgson made the announcement at the same time that he unveiled his squad for Wednesday's game against Norway and England's opening 2016 European Championship qualifier against Switzerland in Basel on September 8.
There were four uncapped players in the squad in the shape of new Arsenal defender Calum Chambers, Tottenham Hotspur left-back Danny Rose, Newcastle United midfielder Jack Colback and Aston Villa midfielder Fabian Delph.
Colback's selection came as a surprise and follows the 24-year-old central midfielder's close-season move to Newcastle from formative club Sunderland.
"I spoke to someone who knows him well and he called him The Ginger Pirlo. It would be nice if he turned out like that," Hodgson said.
"I was impressed with him last year and he has an awful lot to offer. He is a very talented player."
Everton's 20-year-old defender John Stones also earned a recall after being named as a standby player for the World Cup, while Tottenham winger Andros Townsend returned after missing the World Cup through injury.
It is the first squad that Hodgson has named since the World Cup and the first since 34-year-old Gerrard and fellow veteran midfielder Frank Lampard, 36, announced their international retirements.
Another long-serving player, left-back Ashley Cole, called time on his England career after being omitted from the squad for the World Cup.
Glen Johnson, Luke Shaw, Michael Carrick, Ross Barkley, Theo Walcott, Jay Rodriguez and Adam Lallana were among the players who missed out on a place in the 22-man squad due to injury.
England squad for friendly against Norway and opening Euro 2016 qualifier against Switzerland:
Goalkeepers: Fraser Forster (Southampton), Ben Foster (West Bromwich Albion), Joe Hart (Manchester City)
Defenders: Leighton Baines (Everton), Gary Cahill (Chelsea), Calum Chambers (Arsenal), Phil Jagielka (Everton), Phil Jones (Manchester United), Danny Rose (Tottenham Hotspur), John Stones (Everton)
Midfielders: Jack Colback (Newcastle United), Fabian Delph (Aston Villa), Jordan Henderson (Liverpool), James Milner (Manchester City), Alex Oxlade-Chamberlain (Arsenal) Raheem Sterling (Liverpool), Andros Townsend (Tottenham Hotspur), Jack Wilshere (Arsenal)
Forwards: Rickie Lambert (Liverpool), Wayne Rooney (Manchester United), Daniel Sturridge (Liverpool), Danny Welbeck (Manchester United)