Farah, who won the men's 5,000m and 10,000m at the Olympic Stadium, said it was 'great news'.
His wife Tania was heavily pregnant when she joined him on the track after his first triumph three weeks ago.
The Team GB runner had dedicated his medals to his unborn daughters after achieving the rare double and sealing his status as a star of the Games.
Speaking at a press conference in Birmingham, Farah said: "My wife has been holding on so long and it's great that she held on this long and didn't give birth on the track (at the Olympics)."
He said he had been present when his wife gave birth in London yesterday (24 August).
When asked how fatherhood compared with winning an Olympic gold medal, he said: "It's completely different. It's out of your control, it was weird, but as a father I'm very proud.
"To have three kids in the family is going to be exciting. If my wife has another two more twins boys, I'll be a happy man."
Farah also said his stepdaughter Rihanna, eight, was 'very excited' by the arrival of her new sisters.
He said while no names had been picked, they would eventually be inscribed on his gold medals.
"I am actually going to get their names on it, once we've figured out something with the medals - one on each. And then whatever one was born first gets the 10,000m and the other gets the 5,000m one."
Farah, 29, broke the British indoor record for two miles this year and will try to break Steve Ovett's 1978 outdoor mark of eight minutes, 13.51 seconds in Birmingham.
Born in Somalia, Farah spent most of his early life in Djibouti and arrived in London when he was eight. His own twin brother is still in Somalia.