The new 63ha garden is to be set at Worsley New Hall, on the site of a former grand historic garden which has fallen into disrepair.
It will be the RHS' fifth garden and is set to open in 2019, with an aim of attracting one million visitors annually. The garden will be masterplanned and designed by Tom Stuart-Smith.
Councillors expected to face criticism following the decision to help fund the garden, made at an Extraordinary Council Meeting on 16 December.
But they say the garden will create many spinoff benefits, including creating 200 jobs once it opens. Council bosses say Salford can also expect to benefit from around £25m of RHS money coming into the city over the next decade.
Local online magazine the Salford Star has criticised the "cashstrapped" council's spending priorities.