The actor, who plays David Platt in Coronation Street, reportedly slept with promotions girl Sammy Milewski last year after meeting her in a club.
She became pregnant and Shepherd requested a DNA test when 7lb 3oz Greyson was born in January. The People reports that he wants nothing to do with his new son.
The positive result is said to have been a "massive comfort" to Milewski, who hopes that the soap star will contribute to the boy's upbringing.
A friend said: "Sammy agreed to the DNA test at Jack's insistence but she has always known for certain who the father is."
He already has a daughter with childhood sweetheart Lauren Shippey, 2-year-old Nyla.