England have not reached the final four of a World Cup since 1990 and have won the tournament just once, in 1966.
Despite sitting 10th in the FIFA world rankings, Beckham - who won 115 caps for England - feels that Hodgson's squad will feel confident about their chances at next year's showpiece in Brazil.
"I'm always optimistic about when England go into competitions because I've been there, I've felt how it is when you go into a big competition," Beckham told Sky Sports News.
"Roy's come in and changed the team around a lot, introducing a lot of young, talented players to the squad. When you go through a qualifying campaign, there's always ups and downs, it's like a rollercoaster.
"But when you actually reach the competition, once you've qualified, everyone calms down and everyone starts looking forward to the competition that's coming up.
"I think you always go into competitions thinking you're going to win it."
The former Manchester United and Real Madrid midfielder acknowledged the size of the task but picked Tottenham winger Andros Townsend as an example of why England can shock the footballing world.
"It's obviously very difficult because you come up against some of the best countries with some of the best players in the world," he said.
"But we have some young players coming through like Andros Townsend, who has come into the team and there's a freshness now. He is playing without any worries and that's great to see.
"He's a player who hasn't always been in the starting line-up, he's gone out on loan a few times, but he's now one who's established in the England team.
"This is the biggest football competition in the world, with the best players in the world, but we'll see. I hope we can go all the way."
England will find out what group they are in at the World Cup when the draw is made on December 6.
