Singleton, a 6-foot-8 forward, has played parts of five seasons in the NBA, most recently with the Washington Wizards in 2011-12.
He played the 2012-13 season in China with the Xinjiang Flying Tigers, averaging 15.1 points and 11 rebounds in 21 games.
The Knicks will need to cut a player on their 15-man roster once their agreement with Singleton, 33, becomes official. The New York Daily News first reported the Knicks were close to a deal with Singleton on Wednesday.
Singleton should help offset injuries to the Knicks' front line. Tyson Chandler (bulging disk in neck) and Kenyon Martin (left ankle sprain) will miss at least the next two games because of their injuries.
Marcus Camby is doubtful for Thursday's game against Chicago because of plantar fascia in his left foot. So the Knicks need help on the front line as soon as possible.
Singelton was not on an NBA roster after March 1, so he will be eligible for the postseason.
It is unclear at this point who the Knicks will cut once they add Singleton.
Knicks coach Mike Woodson said recently he hoped both veteran big men could return at some point during the playoffs. The Daily News reported the Knicks plan to release Thomas, who will have right foot surgery next week.
The team would not comment on the addition of Singleton.
Ian Begley is a regular contributor to ESPNNewYork.com.