Westphal also retained 78-year-old assistant Pete Carril, the Hall of Fame coach from Princeton who has been affiliated with the Kings for much of the past 13 years.
Elie, a three-time NBA champion as a player, has been an assistant coach in Dallas, Golden State and San Antonio. He spent the last two seasons with the Mavericks while Westphal was an assistant coach and an executive in Dallas.
"He was one of the first guys that I targeted," Westphal said. "He's going to really help us with his defensive intensity."
Robinson was Westphal's teammate in Phoenix and New York during an 11-year playing career. He spent last season as a scout for Washington, but has never coached in the NBA.
Westphal said Carril, the winningest coach in Ivy League history, will be "the one we all learn from."
"He'll be around quite a bit," Westphal said. "He won't travel to all the games, but he'll be a presence at practice, home games and meetings."