The announcement comes one day after Bradley Wiggins became the first Briton to win the Tour de France.
The event could be one of the first major international tournaments to be held in the Queen Elizabeth Olympic Park after the Olympics.
Johnson said: "I want our great capital city to play its own part in the cycling revolution that is taking place by hosting the track cycling world championships in 2016. This is the best sports city in the world and the wonderful velodrome we have built in east London would be packed to the rafters for such an event."
British Cycling with the support of London & Partners’ and UK Sport's major event teams, together with the London Legacy Development Corporation and Lee Valley Regional Park will develop and submit a bid to the cycling governing body, Union Cycliste International. A decision is expected this winter.
Shaun Dawson, chief executive of Lee Valley Regional Park Authority, which will own and run the Velodrome post-London 2012, said: "We are delighted and proud that Lee Valley Velodrome has been selected as the British venue biding for this thrilling event."
Jonny Clay, membership director at British Cycling, said: "Success in our sport has always been anchored in Manchester and that city remains the home of British cycling. In that context it was always going to be tough to consider hosting an international event anywhere else, but we felt the potential impact for the sport and for cementing the reputation of the velodrome in London meant that this time, the Lee Valley velodrome was the right partner for us."
Comment below to let us know what you think.
For more in-depth and print-only Olympics features with official brands, don't miss the next issue of Event magazine by