Gehry, 74, has a special interest in the Maggie's centres because of his close friendship with founder Maggie Keswick Jencks, who died of cancer in 1995.
Maggie was married to Charles Jencks, an architectural theorist who was a friend of Gehry. She was inspired to set up the centres after discovering that there was a lack of emotional support for patients.
Gehry's design for the Maggie's centre in Dundee was praised for the sinuous lines of its titanium roof.
The Maggie's Centre charity has offered up to £900,000 towards the cost of the Swansea centre. Health Commission Wales is also offering £100,000. The charity will appoint professional fundraisers to help meet the expected £115,000 annual running costs.