O'Driscoll has been in good form since returning to action after a knee injury and the 34-year-old's international career is by no means over, but Heaslip has been given the nod to skipper the side.
The decision by Kidney comes after the Leinster vice-captain stepped up to the mark to captain Ireland during the Autumn Internationals.
Ulster captain Chris Henry - who has been named in the extended 39-man squad ahead of next weekend's Wolfhounds game and the 6 Nations opener against Wales - thinks it's the right choice.
Having played for Ireland under the captaincy of both players, he told UTV: "I think Jamie did a great job in November, he rallied us well.
"He did a really good job, so I think it is probably the right decision ..."
Henry added: "Brian obviously had his injuries - he just needs to focus on getting back out on the pitch and playing rugby, so it takes a bit pressure of him too.
"And Jamie, I think he is the right man for it at the moment."
Henry is just one of 11 Ulster players named in the squad.
Lewis Stevenson gets his first call up at international level and Paul Marshall and Darren Cave are among the backs once again.
But first up for Ulster, they're looking for their first win in France this weekend against Castres to secure a home quarter-final in the Heineken Cup.