O'Driscoll has recovered to take his place in Kidney's 39-man squad, which features six new faces, for the RBS 6 Nations as well as the Irish Wolfhounds' clash with England on January 25, although O'Connell has not.
Those six uncapped players include Connacht backs Robbie Henshaw and Dave McSharry as well as Ulster second row Lewis Stevenson, his teammates Paul Marshall and Paddy Jackson, who formed the half-back pairing in the non-capped autumn clash with Fiji, and Leinster's Ian Madigan.
Luke Fitzgerald is also selected despite having played just 124 minutes of rugby for Leinster since April last year. He last turned out for Ireland before the 2011 World Cup.
"I was incredibly honoured when Declan asked me back in November to lead the team in Brian's absence. To lead your country is the ultimate in any sport," said Heaslip, 29.
"To get the opportunity again, considering what an inspirational leader Brian is and the other players who could have been chosen to captain the team, is even more humbling.
"I know Brian as a teammate and as a friend and I will be relying on his and the other players support as we head into the Championship."
O'Driscoll admitted his disappointment at missing out on the captaincy but vowed to support his Leinster teammate in the forthcoming RBS 6 Nations.
"The captaincy has been a big part of my career and life over the last number of years, and while I was naturally very disappointed not to be leading the team in the Six Nations, when I talked it through with Declan I accepted the reasons behind the decision," he said.
"Jamie will do a fantastic job and along with the other senior players in the leadership group, I will be giving him all of the support that he needs."