Redknapp was regarded as favourite for the role following the sudden departure of Fabio Capello in February, before the FA surprisingly unveiled Hodgson on Tuesday. Redknapp, though, insists he is fully supportive of Hodgson ahead of Euro 2012, despite holding a fear that he may never guide the national team to a major tournament himself.
"I don't think it will ever happen now," Redknapp said. "Roy has four years and I hope he sees it out and has great success at the Euros. He will select a squad that is capable of giving it a real go and I think he'll do well.
"I'm fed up of hearing my name mentioned now. I'm history with that job. Roy deserves it, he's got it and I'm sure he'll make a great job of it.
"I'm looking forward to a summer holiday as I've had a difficult year. I'm looking forward to having a break and going away with my wife, before coming back and watching the Euros."
Redknapp was not contacted by the FA over the position, but says he understands the decision and is willing to move on swiftly in order to steer Spurs back toward a Champions League spot next season.
"I'm not disappointed at all, it's done," Redknapp said. "End of story, move on. Get behind the manager and forget about me. They made their minds up, and it's good enough.
"It's saved me making a decision, because I'm very happy at Tottenham. If they'd interviewed me I don't think Roy would have wanted it. I don't think I'd have done either if they were going to interview someone else.
"There's lots of lads about cleverer than me managing lower division clubs. I'm lucky, I'm managing one of the top four clubs in the country. I get very well paid, I've got a fantastic job, so I don't feel anyone owes me anything. I didn't wake up on Monday morning and think: 'What's happened to my life, I'm not the England manager'."