Timberlake, 34, was "ecstatic," People magazine said, adding that mother and baby were doing well.
"My amazing son and his beautiful wife have given us the most precious gift in the world!" Timberlake's mother, Lynn Harless, wrote on Facebook.
"Silas Randall Timberlake! Named after my father and my son! Life is beautiful and we couldn't be happier! God bless you all and thanks for all the congrats!"
Actress Biel, who found fame with US television series 7th Heaven, began dating former boy band N'Sync frontman Timberlake in 2007, after he launched a successful solo career.
The couple married in 2012 in a lavish ceremony in Italy.