While O'Driscoll didn't take any part in the Captain's Run at Twickenham, British & Irish Lions full back Kearney did as he eased fears of his back problem forcing him to miss Leinster's shot at European rugby history.
Kearney sat out last weekend's PRO12 semi-final win over Glasgow Warriors, but will start against Ulster.
"Brian didn't train today, but Rob had a run. He's feeling fairly comfortable and we are confident he will be out there with Brian," said Schmidt.
"It is pretty much 100% they will both be playing and there is no medical reason whey they can't. Brian hasn't had a reaction to the knee operation and the presumption is he will play a full part - and that is certain his presumption."