Kidney boasts an impressive record of his own having enjoyed success at age-group and provincial level, plus he has experience of working with the national team having been O'Sullivan's assistant between 2002 and 2004.
Kidney was in charge of the Ireland Under-19 team that won the 1998 World Cup and included the likes of O'Driscoll, Donncha O'Callaghan and Paddy Wallace.
He has led Munster to four Heineken Cup finals and, after defeats in 2000 and 2002, he delivered the trophy in 2006 with victory over Biarritz at the Millennium Stadium.
Kidney returns to Cardiff on May 24 chasing more European glory for Munster before turning his attention to the national cause.
In 2006, Ireland were second in the world but they head to New Zealand and Australia this summer having slumped to eighth place in the rankings.
O'Driscoll said: "Declan has the CV to match the criteria for any international coach.
"He has had success with the national team at age level, he has had great success with Munster, he has been assistant coach under Eddie O'Sullivan back in the 2003 World Cup. He ticks all the boxes.
"From what the guys at Munster say, he has taken a little bit of a step back from the coaching role and he is the man who now puts it all together.
"He knows how to get the best out of his players and his coaches. If he does that with Ireland hopefully we can get back to the heights we hit 18 months ago."
Due to his Heineken Cup commitments with Munster, Kidney will not take up his new post until after Ireland return from the summer tour to New Zealand and Australia.
The Irish Rugby Football Union plan to appoint an interim management team for the trip, which begins with a fixture against the Barbarians in Gloucester on May 27.
Unusually, Kidney will play no part in the squad selection or preparation for the tour.
Ireland A coach Michael Bradley is widely expected to take charge, and O'Driscoll admits it is not the ideal scenario.
"Ideally you would want the coach to be in as soon as possible," he said.
"It has felt a little like the process of appointing the new Irish soccer coach (Giovanni Trapattoni) for a while, though not quite to the same extent.
"I think Declan realised his focus is on Munster at the moment and he can't give any time to Ireland. It does give him the chance to see things from the outside before he does come and join the squad."