A poll carried out on behalf of the Mayor's Office for Policing and Crime (MOPAC) suggested 68% of Londoners were behind the measure. Boris Johnson said there was "broad support".
However more than 37,000 people have signed an online petition against the purchase.
The cannon will be purchased if Home Secretary Theresa May licences them.
The Metropolitan Police and Mayor of London Mr Johnson want to buy three cannon from Germany for Â£90,000.
They have been linked to causing broken bones and blindness.
Mr Johnson said: "No-one wants to see water cannon routinely deployed on the streets of London but having carefully weighed up all the evidence, I have concluded there is broad support amongst Londoners for the use of this measure by the police in limited circumstances.
"However, it is critical that Londoners are assured that there are robust safeguards in place before seeing water cannon in action."
The mayor said he would now write to the Home Secretary to support the request for water cannon.
The independent poll conducted by TNS questioned 4,223 people and found 52% said they would have greater confidence in the Met Police's ability to respond to serious public disorder if water cannon were available.
In addition the mayor carried out a six-week consultation in January and February to gather the views of Londoners on the use of water cannon.
There were 2,606 consultation responses received via email and 4,048 email petition responses. From the email consultation 59 people supported the introduction of water cannon.
Concerns were raised by more than 2,500 email respondents and more than 4,000 people responded to the "Boris: stop the water cannon" and the "No to water cannon" email petitions.
Respondents also mentioned a change.org petition with more than 37,000 signatures against the proposals.
London Assembly member Jenny Jones, of the Green Party, said: "He has ignored the members of the public who responded to the consultation, and the views of the Assembly including members of his own party and team, to push ahead with his plans for this weapon."
Water cannon have been used in Northern Ireland but they are not currently authorised in Britain. The Home Secretary must approve their introduction in England and Wales.
An ethics panel, headed by barrister Lord Carlile, will be put in place to look at when water cannon should be used, if they are licensed by the home secretary.
She has refused to provide central government funding for the machines in London.
A Home Office spokesperson said: "It is for Chief Constable David Shaw, as the national policing lead, formally to request that water cannon be authorised for use and present the necessary information for the home secretary to make a decision. We await that request."

Clive Williams, 69, was headmaster at Ashdown House Preparatory School in Forest Row, East Sussex for more than 25 years before he left in 2003.
He was questioned by Sussex Police about alleged sexual assault and child neglect offences against pupils.
Mr Williams was not charged and was bailed until 11 November.
Police said a 69-year-old man was arrested at an address in Barcombe, near Lewes, on Wednesday and a computer and documentation were seized.
The man was not named but BBC sources confirmed he was Clive Williams.
"During January this year we were contacted by a firm of solicitors representing a number of clients who have reported to them that they were sexually and physically assaulted by staff, whilst they were pupils at Ashdown House School near Forest Row in the 1970s," a police spokesman said.
"We have since been in contact with 20 people reporting offences against them, including those clients.
"Most have already been interviewed by officers from our specialist Child Protection Team in East Sussex.
"The investigation continues and now spans a period from the late 1960s to the early 1980s."
Sussex Police said there were no current safeguarding issues at the school.
Ashdown House has been owned by the Cothill Educational Trust since 2009.
The trust said in a statement in January, it understood that it may be the subject of legal proceedings relating to episodes of abuse, said to have taken place between 30 and 40 years ago.
"The trustees are deeply saddened about those matters and wish to do everything they can to assist any former pupil who has been affected," it said.
The Mayor of London has agreed to support the Met Police's call for water cannon to be purchased.
[NEXT_CONCEPT]
The former headmaster of a prep school attended by London mayor Boris Johnson, has been arrested on suspicion of historic sex assaults.