The Knicks have called an afternoon news conference at which Smith will be given the award, the source said. The news was previously reported by The Associated Press.
The eighth-year guard has averaged 18.1 points in 80 games, all off the bench. He had 29 games in which he scored 20 points as a reserve, tying him with the Clippers' Jamal Crawford for the NBA lead.
Smith helped the Knicks win the Atlantic Division title for the first time since 1994. New York is the No. 2 seed in the Eastern Conference and leads the Boston Celtics 1-0 in their first-round playoff series.
It's the second individual award in two years for the Knicks, following Tyson Chandler's Defensive Player of the Year honor last season.
Despite not making a start, Smith was one of the Knicks' most important players. He played more than 40 minutes seven times and was often their only scoring threat behind Carmelo Anthony.
Crawford seemed to be the favorite for most of the season before Smith overtook him with his strong play down the stretch. He had three straight 30-point games from March 26-29, the first time that was done by a reserve since Milwaukee's Ricky Pierce in 1990.