The 33-year-old centre, who skippered Ireland to a Grand Slam in 2009, admits that he won't be around at the next World Cup and that the time is therefore right for Ireland to appoint a new leader.
"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," said O'Driscoll.
"I've always known that the Rugby World Cup in 2015 was most likely a bridge too far for me, so at some point a player, who will most likely be there for the tournament, needs to build that captaincy experience.
"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."
Kidney believes the decision will allow O'Driscoll to focus fully on his recovery from injury, with the Ireland boss suggesting that the appointment of Heaslip was made as much with the present as the future in mind given that BOD has played very little rugby since the 2011 World Cup.
"Obviously he'd be very disappointed, Brian has always told you what an honour it is to captain Ireland and that will never change. He accepts my reasons for doing it," added Kidney.
"I don't think people realise sometimes the amount of weight that would be on a captain's shoulders and Brian's been hugely generous to the team and I just feel that now is the right time to allow him to concentrate on himself, to get himself right."
As for Heaslip, the Lions Test No8 led Ireland against South Africa, Fiji and Argentina in November and is delighted to have been given the nod to continue his captaincy ahead of the Six Nations opener in Cardiff on February 2.
"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.
"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."