England sit one point clear of Ukraine and Friday's opponents Montenegro at the top of Group H with two qualification fixtures remaining.
Rooney admits he originally backed Harry Redknapp to succeed Fabio Capello as England boss but praised Hodgson for his handling of the role.
|20/1||Wayne Rooney is 20/1 with William Hill to score a hat-trick against Montenegro
"He was doing a tremendous job with Tottenham and everyone thought Harry was going to get the job. The way it was made out, it looked like he was nailed on. But then, obviously, Roy's popped up.
"The FA have gone with Roy and, for me, I feel now that was the right decision.
"I feel he's going to take us to the World Cup. It's probably the most I've enjoyed working for any England manager. His man-management is really good. He really speaks to us. And he's shown a lot of trust in me, both on and off the pitch."
At 26, Rooney has won 84 caps and scored 36 goals for England and the Manchester United striker is looking to better Sir Bobby Charlton's record of 49 strikes for the national team.
"I believe I can. I’m actually a bit disappointed with my record. I feel I should’ve scored more for England," Rooney added.
"If I keep playing, keep scoring and trying to help the team, I believe I can get to that 50-goal mark, which would be an unbelievable achievement."
Rooney insists he is excited by England's final qualification fixtures against Montenegro and Poland and is hoping he can prove critics of Hodgson's side wrong.
"Over the last five or six years this is probably the most excited I've been about England games," Rooney continued.
"We've got two games at Wembley, we need six points, and it's great. There have been a few doubters in recent games and we have to prove we're good enough."