Aston Villa boss Tim Sherwood attempted to sign Begovic from Stoke and would likely have immediately installed him as first choice at Villa Park, but the Bosnian instead chose to join Chelsea as back-up to Courtois.
Begovic is adamant he did not move to Stamford Bridge for money, however, and is bullish over his prospects of regular first-team action with the Blues.
“Obviously everyone has their opinion, but for me it was more of a challenge to try something different,” he said.
“I think I was at that stage where I want to test myself against the best and that’s ultimately what I’ve come here to do.
“Even after the first week you can see the quality here and how they can improve you with the levels and demands here.”
On the battle for the No.1 spot, Begovic added: “There have been no guarantees. The challenge, the manager Jose Mourinho and players that are all here, was what attracted me and that was a big part of my decision.
“I’ll back myself, absolutely. I’ll be keeping my head down and working hard to see how I can help this team in the future. Obviously I want to try and get as many games as I can, and now I’m competing for trophies.
“I want to test myself against Thibaut; he’s one of the best goalkeepers in the world, but I believe in myself. Hopefully every time I can show everybody what I’m all about and ultimately help this team. We all have to play our part, and at a club like this I think you get to do so.”