The actor, best known for playing Nelson Mandela in last year's biopic The Long Walk To Freedom, tweeted that his partner, make-up artist Naiyana Garth, had a baby boy yesterday.
Elba, who also starred in US cop drama The Wire and British crime series Luther, said they have named their Winston after his late father, who worked for the Ford motor company.
The 41-year-old Londoner tweeted a picture of the tiny baby's hand clutching his own to his one million followers on the social network.
Along with it he wrote: "My Son Winston Elba was born yesterday. Truly Amazing :-)."
He already has a daughter, Isan, with his ex-wife Kim.