"Signing a player of Tyson's caliber, with championship experience, to this roster, is an opportunity we could not pass up," Knicks interim general manager Glen Grunwald said in a statement.
Chandler, 29, averaged 10.1 points and 9.4 rebounds in 74 regular-season starts for the NBA champion Mavericks last season.
He has spent 10 years in the NBA with Chicago, New Orleans, Charlotte and Dallas.
"Tyson will be the anchor to our defense," Knicks coach Mike D'Antoni said. "The trio of Amar'e Stoudemire, Carmelo Anthony and Tyson makes one of the most formidable frontlines in the entire league."
Dallas traded a 2012 second-round draft choice to Washington and the draft rights to forwards Ahmad Nivins and Giorgos Printezis to New York.
The Mavericks also gained a conditional future second-round draft choice from Washington.