The midfielder left Derby for the Clarets last week.
O'Neill said: "It's a good move for Jeff, it's Premier League football for him and I'm sure he is very, very excited by it.
"I want him, obviously, to leave that to the side now. He got the deal through before the deadline and now it's total concentration on this game here for tomorrow. But overall, I think Jeff should prove himself in the Premier League."
It has been a whirlwind few days for Hendrick, who was given permission to leave the Republic camp last week as Burnley formalised their interest in him, but was back in time to play as a half-time substitute in Wednesday night's 4-0 friendly victory over Oman in Dublin.
Hendrick said: "Obviously I'm delighted I got the move. I was waiting a few weeks for it to get done. After the summer I had, I wanted a crack at the Premier League and I'm happy it's done.
"But as the boss said, my main focus is the game tomorrow night. They are exciting times, but I've got to focus on the game tomorrow."