The team announced the signings Thursday, along with the re-signing of forward Lou Amundson.
The 7-foot-3 Porzingis was the fourth overall selection in the recent draft and played professionally for Cajasol Seville in Spain the past three seasons. At the NBA summer league in Las Vegas this month, the 19-year-old averaged 10.5 points in four games.
Grant, a 6-4 guard, was the 19th overall pick after averaging 14.6 points and 5.8 assists in four seasons with Notre Dame. In his senior season, he averaged 16.5 points and 5.8 assists in 38 games. In five summer league games, Grant averaged 11.8 points and 4.8 assists in five games.
Amundson averaged 6.0 points and 6.0 rebounds in 41 games after signing with the Knicks in January.
Also Thursday, New York waived guard Ricky Ledo. He averaged 7.4 points, 2.8 rebounds, 1.5 assists and 19.4 minutes in 12 games for the Knicks last season.