Goalkeeper Begovic and midfielder Wilson have both signed three-year contracts that will keep them at the club until 2011.
Begovic, who has yet to make a first-team appearance, said: "It's a nice honour to be wanted here. Competing for a place in the team is one the most difficult things about being a keeper.
"But being patient is just a thing that goalkeepers have to be."
Wilson, 20, added: "I've just got to work hard in pre-season and see where it goes from there.
"But the plan is to push on and hopefully break into the first team."