The £135m programme will operate on a universal basis and run throughout the 2023/24 academic year.
New figures show how many children in each borough will benefit, with the highest number in Barnet, where 13,495 pupils will receive the meals, followed by Bromley (13,321) and Redbridge (13,028).
The borough with the fewest expected recipients is Kensington and Chelsea, with just 2,539 children anticipated to get the lunches.
While not technically a borough, the programme is also being rolled out to schoolchildren in the City of London, otherwise known as the Square Mile. A total of 113 pupils will be entitled to the meals there.
City Hall says that thanks to the policy, families will save “upwards of £440 per child”.
The Government already provides free school meals on a universal basis for children up to and including Year 2.
After that point, the Government only provides lunches to children from households receiving certain benefits. For households on universal credit, they must earn less than £7,400 a year - after tax and not including benefits, and regardless of the number of children in the family - in order for their children to be eligible for the meals.
The lunches administered through the mayor’s scheme will provide for children in Years 3-6.
Five London boroughs - Islington, Newham, Southwark, Tower Hamlets and Westminster - all currently provide universal free school meals for all primary school children.
City Hall said that funding is still being allocated to the five boroughs as if they were not currently providing the meals - with the intention being that they can use the funds to support other means of helping families with the cost of living crisis.
Mr Khan said: “I know from personal experience what a lifeline free school meals can be, which is why I’m determined to do all I can to help families across London who are struggling during this escalating cost-of-living crisis.
“I’m proud that hundreds of thousands of children will benefit from the unprecedented funding when they return to school after the summer holidays, and that parents in every borough will know their children are receiving a good meal at lunchtime.
“By ensuring children don’t go hungry in the classroom and helping their families, we can build a better and more prosperous city for all Londoners.”
City Hall said at the time of announcing the policy: “This is one-off funding from additional business rates income. Sadiq is clear that he is only able to provide help that should be coming from the Government for one year.”
But Susan Hall, the Labour mayor’s Conservative rival in next year’s City Hall election, has said she would keep the policy in place through to the 2024/25 school year “at a minimum”, if she is elected.
Though she has called the policy “imperfect” - saying that it could have been better targeted at “those most in need” - she has pledged to keep the programme going on a universal basis “for as long as the cost of living situation requires it”.
The number of children expected to benefit in each borough is as follows:
Barking and Dagenham - 9,749
Barnet - 13,495
Bexley - 10,377
Brent - 11,502
Bromley - 13,321
Camden - 3,606
City of London - 113
Croydon - 12,723
Ealing - 12,581
Enfield - 12,202
Greenwich - 9,947
Hackney - 6,140
Hammersmith and Fulham - 3,677
Haringey - 8,528
Harrow - 9,976
Havering - 10,653
Hillingdon - 12,435
Hounslow - 10,056
Islington - 4,246
Kensington and Chelsea - 2,539
Kingston upon Thames - 6,655
Lambeth - 7,047
Lewisham - 9,495
Merton - 6,680
Newham - 12,611
Redbridge - 13,028
Richmond upon Thames - 8,124
Southwark - 8,008
Sutton - 8,826
Tower Hamlets - 8,294
Waltham Forest - 9,818
Wandsworth - 7,361
Westminster - 3,064