Wittman was named interim coach after the Wizards fired Flip Saunders in January when the team was 2-15. Washington won eight of its last 10 games and was 18-31 overall under Wittman.
"We are excited to bring Randy back as head coach and give him the opportunity to build on the positive momentum that the team showed under his leadership last season," Wizards President Ernie Grunfeld said in a statement.
"We were very pleased with the development of our young players and the commitment to winning he instilled despite taking over the team under difficult circumstances."
Wittman previously coached at Minnesota from January 2007 through Dec. 8, 2008, and Cleveland from 1999-2001. He had an overall record of 118-238.
"I'm thrilled to be returning to work with these players and this organization," Wittman said. "I felt that we made significant progress throughout last season and we are all looking forward to having a full summer, training camp and season to continue to improve this team."
The Wizards learned last week they will have the third overall choice in the NBA draft in June 28.