There were minor concerns after Bell took a blow to the shoulder when practising at the nets on Tuesday, while Bresnan was forced to miss the first Test in Brisbane due to a stress fracture of the back.
"[Bell's] fine. It's just one of those places on the shoulder - it just goes dead for a few hours." Cook said in a press conference. "He's back training today.
"[Bresnan]'s fully fit. He's come back amazingly well from his injury in his back, his stress fracture. He played that last game for the EPP [a week ago], and came through that totally unscathed.
"He's ready and available for selection. One of his great skills is he does bowl a lot of overs in Test matches. He's done that in the past. If we decide to go Bresy, he's ready to play."
The second Test gets underway at the Adelaide Oval on Thursday with Australia holding a 1-0 lead.