Murray has been catapulted into Sunday's World Cup opener against the United States at Stadium Taranaki despite his lack of experience in what is a bold selection by coach Declan Kidney.
The 22-year-old, the squad's youngest player, only established himself as a first-team regular for Munster this year, but he has already earned O'Driscoll's approval.
"Conor is a confident young man. We were talking about him behind his back, about his probable man of the match performance in the Magners League final," he said.
"Although David Wallace picked the award up, the boys thought Conor was outstanding. He's shown great form and presence in training.
"I have no doubt he's up to the challenge. He's definitely got the right temperament for this.
"I've got to know him a little bit better as a person over the last few weeks. He's coming out of his shell a little bit.
"He's confident, but not arrogant. He has good inner belief. His career is starting on a pretty good footing.
"It's not easy for a young guy like him to come into a squad. I was that person once upon a time.
"It's difficult to be yourself. You tend to stay in your shell a bit more and let others do the talking.
"But the more confident you get with your surroundings, your personality shines through.
"He's a lot more confident in the company of the Munster guys but we've seen signs that he's coming out of his shell.
"I've had some good laughs with him over the last week and he's a nice young fella."
O'Driscoll is looking forward to his reunion with Eddie O'Sullivan, the USA coach who was axed by Ireland in 2008 following seven successful years.
"I enjoyed working with Eddie. It was a long period in my international career," said the Leinster and British and Irish Lions centre.
"He had a huge part to play in my career. He did some great things for Irish rugby and was unfortunate not to win a Grand Slam.
"But he shaped the team to go on and achieve that. He deserves credit for that.
"When it comes to how much he knows about us, you can over-read things. Players evolve and won't necessarily be the same as in 2008.
"Aspects of our game have changed. Plenty of new personnel have come in since he left."
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