She will now carry their IVF baby for nine months and give it up to the couple after birth.
Charity worker Mrs O'Driscoll, 38, suffers from Mayer-Rokitansky-Kuster-Hauser syndrome, which means she was born without a womb.
Surrogacy or adoption seemed the only hope of a child for her and business consultant Mr O'Driscoll, 39.
Their lives were transformed after meeting surrogate mother Mrs Housley and her husband Dennis, 37, a helicopter engineer.
They met the O'Driscolls through not-for-profit organisation Surrogacy UK and they spent about seven months getting to know and trust each other.
Mrs O'Driscoll's eggs were fertilised with her husband's sperm and placed in Mrs Housley's womb. She is now 29 weeks pregnant and due to give birth in October.
"I don't want any more babies of my own. I've had mine and they have brought us happiness and everything else. This way everybody wins. I get to be pregnant which I love, and somebody else gets a baby that they want very much," the Daily Express quoted Mrs Housley, from Portsmouth, Hants, as saying.
Mrs O'Driscoll, from Highgate, north London, said: "I took drugs to stimulate my egg production. Of the resulting seven embryos two survived and were transferred into Kate.
"Two nail-biting weeks later Kate, Andrew and I were all together in a coffee shop in central London when the call came through that she was pregnant and we all burst into tears.
"That cloud will not necessarily lift at once just because this trial has come to an end."