Chairman of the London Fire and Emergency Planning Authority, Assembly Member James Cleverly said:
"I'm pleased that the Mayor has backed me and given his full support to the Fire Commissioner's plan. Like all fire brigades, we need to save money without compromising our ability to protect people.
"The proposals are responsible and proportionate to the significant reduction in fire risk. Labour, as always, refuse to acknowledge the need for reform and, at a time of considerable financial constraint, have insisted on increased budgets.
"The Mayor's decision means that we can finally provide clarity and stability to our firefighters, who over the last year have suffered from the prolonged uncertainty of this unnecessarily protracted process."
When he published his revised proposals last month, Mr Dobson said:
"We have to acknowledge that the number of fires we attend has gone down by half in the last 10 years, and our latest figures show that fires continued to fall at the same rate last year.
"Under my revised proposals, response times in London will remain amongst the very best of any emergency service in the UK and firefighters will continue to carry out community safety work to prevent fires at the same level as they do now.
"Fire stations and fire engines do not stop fires happening - proactive prevention work does."
London's Fire Commissioner, Ron Dobson, had originally proposed closing 12 fire stations, reducing the number of fire engines by 18 and cutting 520 jobs.
A series of public meetings and other consultations were made, resulting in changes to the original plans, but they were still rejected by the fire authority.
In a letter to the authority's chairman, James Cleverly, the Mayor said action had to be taken so that savings could be made, otherwise the authority's spending for 2014/15 would be greater than its resources.
"This eventuality would not represent sound stewardship of public funds and would place both the Mayoralty and the authority in an unacceptable position," he said.
The Mayor warned that further delays to implementing the commissioner's proposals would increase the likelihood of compulsory redundancies.
"I am also mindful of the desirability - which I know LFEPA members share - of avoiding compulsory redundancies for firefighters. Further delays to the implementation of the Commissioner's proposals will increase the likelihood of compulsory redundancies."
Mr Dobson has stressed that safety standards would not be affected by his proposals, which have been opposed by the Fire Brigades Union.
A spokesman for the London Fire Brigade said: "The authority has now received and is considering the Mayor's direction."
London's Mayor has given the go-ahead for fire station closures and hundreds of job cuts among firefighters in the capital to make savings of over £28 million over the next two years.
The fire authority had narrowly rejected the controversial proposals after Labour, the Greens and Liberal Democrats united to oppose the plans, leaving the Mayor to make a decision.
Boris Johnson has now directed the authority to implement the cuts, which will see 10 fire stations close, the number of fire engines reduced by 14, two fewer fire rescue units, 552 jobs axed and minimum crewing levels on fire rescue units reduced from five to four.
The Mayor said he wanted the plans implemented by September 16.