The cash will be made available over three years and is part of £17.3 million awarded to 32 boroughs in the capital as part of the Borough Cycling Programme.
The scheme will offer bespoke training for cyclists and provide Safe Urban Driver courses for 15,000 motorists across London.
Bexley Council cabinet member for environment and public realm, Councillor Gareth Bacon, said: "I'm delighted we were successful with our bid for money to help us encourage more people to cycle more safely and more often in Bexley.
"This money will help us provide more cycle training for adults and children, road safety training for van and lorry drivers, cycle parking across the borough and some small cycle grants for schools who are encouraging students and staff to cycle more.”
Bexley is still waiting to hear whether it will be granted funding to help the borough become a mini-Holland for cyclists.
The Mayor has set aside £100 million to be shared between a small number of selected outer London boroughs and Bexley remains on the shortlist after putting forward its final stage bid at the end of last year.
Mr Johnson said: "Making some of this money available directly to the boroughs will help ensure that cycling developments reach communities across the capital.
"These local schemes will add to the measures we’ve already announced, including enhanced cycling superhighways, urban ‘quietways’ for more cautious cyclists, and turning some outer London boroughs into mini-Hollands."
Ideas designed to get residents dusting off their old boneshakers include redesigning town centres to make them "genuinely excellent" for cyclists and building a network of cycle paths "radiating out from the town centre" alongside other travel routes.
Cycle superhubs offering secure cycle parking at railway stations and redesigns of problem junctions are other proposals put forward.