The Knicks confirmed Tuesday afternoon that they had signed Galloway for the remainder of the season but didn't include any information on his contract status for the 2015-16 season.
Galloway's second 10-day contract with the Knicks expired earlier Tuesday, so he had been free to sign with any team.
His contract for the 2015-16 season contains a partial guarantee, according to league sources. Galloway has impressed the Knicks' coaches since being signed to his first 10-day contract Jan. 7.
Galloway, who played with the Knicks' summer league team and their D-League team in Westchester, is averaging 12 points per game in his first eight games with the team. He is also producing three assists and pulling down four rebounds per game while shooting 43 percent from the field.
After losing 16 straight games, New York has won three of four entering Wednesday's game against the Oklahoma City Thunder, with Galloway emerging as a rare bright spot for the Knicks.
Amundson's second 10-day pact expires Thursday while Thomas' second 10-day deal ends Friday. To retain each player, the Knicks have to sign them to a contract for the remainder of the season.