Darke will move up from deputy chief executive from January 1, 2009.
King will continue to work with British Cycling as an executive director and focus on external projects linked to London 2012 and other stakeholders.
Peter Cookson, the president of British Cycling, said: “I would like to thank Peter King for the superb job he has done over the last 12 years.
“It is no exaggeration to say that he has been pivotal in transforming British Cycling from near-bankruptcy to a world-leading governing body with a reputation for consistently delivering on its objectives.
"Thanks to Peter, British Cycling is recognised at the highest levels of Government as a sound, effective, and reliable body, and the benefits of this can be seen in the achievements and developments in our sport over the past 12 years.”
Drake has worked with British Cycling since 1996, when he was a consultant on the development of young people's programmes in schools and clubs.
This laid the foundation's for British Cycling's successful Go-Ride youth coaching programme.
From 1998, Drake led the development and funding submission for the World Class Start and Potential programmes to support British Cycling's vision of becoming the world's number one cycling nation by 2012.
This led to the creation of British Cycling's renowned talent identification and development programmes.
In 2000, Drake continued this work when he as was appointed as national talent co-ordinator and implemented the Talent Team programme.
This has nurtured the likes of Beijing Olympic medallists Steven Burke and Ed Clancy along with riders such as Lizzie Armitstead, David Daniell and Anna Blythe who are now emerging as athletes with the potential to win medals at London 2012.
Since 2004, Drake has had responsibility for all British Cycling's Sports Council funding submissions and has been the driving force behind the current 2005 to 2009 'UK Wide One Stop Plan', which has brought unprecedented growth in the sport at all levels.
Drake said: “I am both delighted and proud to step up into the role of chief executive of British Cycling and lead the organisation into its next phase of expansion and growth through to and beyond London 2012.
"Peter has made a unique contribution to British Sport in his tenure as CEO of British Cycling, which is a hard act to follow, and I’m looking forward to continue to work with him in his new role.
“It’s a unique moment in time for cycling and British Cycling in the UK given the successes in Beijing, the growth in the sport, the contribution cycling has to make to so many Government agendas and of course London 2012 on the horizon.
“British Cycling has fantastic clubs, members and volunteers all of which have made an invaluable contribution to our current international success and growth to date.
"They will undoubtedly underpin the plans and vision going forward as we continue our journey to replicate our more medal success with more people participating in cycling.”
King said: “I am pleased that the board has accepted my recommendation that Ian should take up the role of chief executive.
"He has been my deputy for more than a year, during which time he has demonstrated that he is the right man to lead British Cycling in delivering the next four year plan which he has himself masterminded.
“When I wrote my survival plan for British Cycling in 1997 I started with my own personal mission statement.
"This was to be able to hand over, to the right person and at the right time, the best run governing body in British sport.
"In my assessment we are now the best run governing body in British sport, the time is right to hand over the helm and I am able to do so now to the right person.”
British Cycling performance director Dave Brailsford said: “Over the past 12 years, Peter has put the structures in place and led British Cycling to its current success.
"Having worked alongside Ian for the past two Olympic cycles it gives me great confidence as we look towards London 2012 that he is now stepping up to the role of chief executive.
"He has the necessary knowledge, skills and attributes to provide the required leadership and support to ensure British Cycling continues to perform at the highest level on the world stage. London 2012 presents a once in a lifetime opportunity for all sport in the UK and in Ian we have the right person to capitalise on that for cycling in all its forms.”