The babies were born to a surrogate mother, the rep, Alex Dubee, tells the Associated Press.
Bassett, 47, starred in movies such as 1998's How Stella Got Her Groove Back and the 1993 Tina Turner biopic What's Love Got to Do With It. Vance, 45, plays district attorney Ron Carver on NBC's Law & Order: Criminal Intent.
The couple have been together since the fall of 1996, when Vance ran into longtime acquaintance Bassett at a play in Los Angeles. The two actors began talking, went out on a few dates and quickly fell into a serious relationship. "We're like old friends who all of a sudden looked up and said, 'Hmmm ..., ' " Vance told PEOPLE at the time. "Gradually it dawned on us that we like each other."