The documents also show that a request for the government to fund the controversial purchase has been rejected by the home secretary,Theresa May.
Public consultations on the deployment of water cannon will begin within weeks and a formal decision made next month.
Water cannon have not previously been available to police on mainland Britain, and their use has been limited to Northern Ireland.
In a letter sent on Monday by Boris Johnson to May, the London mayor explains his reasoning, saying it is a direct result of the 2011 riots that started in London before spreading, becoming the most serious and widespread riots to hit England in decades.
Ultimately the home secretary has final say on the acquisition of water cannon for use in mainland Britain. Critics warn it is a step towards the militarisation of the police and could be used to stifle the democratic right to protest.
In his letter, dated 6 January 2014, Johnson writes: "Following the disorder in August 2011, both the Metropolitan police service and Her Majesty's Inspectorate of Constabulary stated that there are some circumstances where water cannon may be of use in future.
"Following briefing by the [Met] commissioner I am broadly convinced of the value of having water cannon available to the MPS [Metropolitan police service] for those circumstances where its absence would lead to greater disorder or the use of more extreme force."
The Met commissioner, Sir Bernard Hogan-Howe, has pledged that water cannon would be "rarely used and rarely seen", the letter says.
His letter to May, Johnson then discusses funding: "Finally, I am aware that you have declined to make funds available for purchasing the interim water cannon solution as a national asset.
"Subject to the public engagement process … I am happy to make the necessary funds available to the MPS for the most economical interim solution that allows the commissioner to meet his desire to prevent disorder on the streets. I would expect to do this in February, following the [public] engagement."
The latter adds that there is public support for the deployment of water cannon.
In another letter, written on Tuesday by Stephen Greenhalgh, deputy mayor for policing, says a formal decision to go ahead with water cannon will be made next month.
Greenhalgh wants public consultation to begin within weeks, which will involve public meetings and talks with MPs, councillors and what he describes as "stakeholders".
The mayor's office says water cannon would only be used in "the most extreme circumstances".
Greenhalgh's letter was written to Labour's Joanne McCartney, chair of the London assembly's police and crime committee.
The letter says: "In order to ensure that water cannon is available by next summer, something which the commissioner has been calling for, it is important that the process of engagement starts soon."
The Green party London assembly member Lady Jones said: "Allowing water cannon on the streets of London is a step in the wrong direction towards arming our police like a military force, and it goes against our great tradition of an unarmed police service.
"People have a democratic right to protest and my fear is that once the mayor allows these weapons on to our streets we will see them being used against people exercising their legal right to protest."
It is believed the Met are in talks with German companies about supplying water cannon in time for this summer.
The Met has approached companies about hiring or buying second-hand water cannon from overseas to have the machines available as soon as possible.
The Met is interested in acquiring around three units.
In a letter to Jones, assistant commissioner Mark Rowley detailed the training required. He wrote in July 2013 that no more than 20 staff would need to be trained in the use of water cannon and another 200 riot officers would need to be trained in how to quell disorder while working alongside water cannons.
Rowley's letter said the use of water cannon would require authorisation by an officer of the rank of commander.
The home secretary has already signalled her sympathy for the controversial tactic.
Some within the Met have privately told the Guardian they are sceptical about the need and effectiveness of water cannon on London's streets. They say streets here are much narrower than in Europe, where water cannon are already in use, thus making them less effective and potentially vulnerable to capture. They also say water cannon fire jets that could prove indiscriminate and strike innocent members of a crowd.