Frank, who was the head coach of the New Jersey Nets for parts of five seasons, takes over in Detroit following a 57-107 mark over two seasons under Kuester.
The Pistons struggled to a 30-52 record last season.
"We went through a very extensive process, interviewed a lot of candidates. It was a very meticulous, detailed process that we went through," Pistons President Joe Dumars said. "When it was completed, at the end of the day it was a very clear choice that Lawrence was the best guy."
Frank took over as Nets coach in January 2004 and immediately guided them to 13 straight victories, setting an NBA record for the most consecutive wins by a head coach to begin a career.
New Jersey made the playoffs four straight times and won the Atlantic Division twice under Frank.