The actor explained to reporters that the duo first started communicating following the release of Anderson's breakthrough film.
"I'll take credit for initiating our friendship, because I wrote him a letter after I saw Rushmore. It was full of appreciation for that film," the actor quipped, reports Flicks and Bits.
Norton further explained: "That [letter] sort of initiated a correspondence that we've kept up over the years - without actually seeing each other that much. It was one of those things, you hope and you wait and then something comes together.
"When he did give me a ring and say, 'I've written something that I'd love you to look at a role in', I just said, 'I'm in!' He said, 'Well, read it, it's odd'. I said, 'I don't care, lets do it'."
Norton also said that it was a true pleasure to work with his Moonrise Kingdom co-stars Bill Murray, Bruce Willis and Tilda Swinton.
"It's a dream to be in a company of actors. I think all us started out reading about Orson Welles and his Mercury Theatre, the group theatre," he said.
"Any of those great ensembles that worked together, there's a romance to that when you're an actor, I used to dream a lot about how fun it would be to be in a troupe like that. I think Wes has obviously over the years put together one of the great troupes in modern cinema."
Norton recently told Digital Spy that he especially had fun working with Harvey Keitel.
Moonrise Kingdom is now playing in cinemas.
Watch a trailer for Moonrise Kingdom below: