The 41-year-old Golden Globe winner's child was born on April 17, reported People magazine.
The British actor and the star of 'The Wire' shared a snapshot of their tot, which showed the newly born's tiny fingers touching his own.
"My son, Winston Elba, was born yesterday. Truly amazing," Elba Tweeted yesterday.
Winston is the second child for Elba, who most recently starred in 'Nelson Mandela in Mandela: Long Walk to Freedom'. He also has a 11-year-old daughter Isan.