The appointment came on the same day Bill Carmody left the Ivy League school to become coach at Northwestern of the Big Ten.
This will be the first head coaching job for the 34-year-old Thompson, an assistant the past five seasons at Princeton the first under Pete Carril and the last four under Carmody.
"He's got a challenge," John Thompson said Wednesday during the "The John Thompson Show," his WTEM sports radio talk program in Washington. "I'm proud as a father."
Princeton scheduled a news conference for Thursday to introduce the younger Thompson.
Thompson has three starters returning from a team that went 19-11 last season, losing in the first round of the NIT to Penn State.
However, the Tigers sustained a major loss a little more than a week ago when unanimous All-Ivy League center Chris Young signed a baseball contract with the Pittsburgh Pirates.
Unlike the NCAA, the Ivy League does not allow athletes who sign a professional contract in one sport to play in another.
"He's well respected," Young said of Thompson. "He's a good guy and he knows what he is doing. He's very easy to talk to. I think he'll be a players' coach."
Young thinks Thompson won't make many changes in Princeton's patient style of basketball which stresses defense, 3-point shooting and those backdoor layups.
However, Thompson will have to find a way to compensate for the lack of size with Young ineligible.
Thompson, who played at Princeton, graduated in 1988. A forward, he was co-captain in his senior year and shared the team MVP award as the Tigers went 17-9.
The older Thompson was at his son's Princeton home during his broadcast. He laughed about all the telephone calls he received from his son, complaining about how much he hated things during his first two years at the school.
However, that all changed in his final two years, Thompson said, and no one could say anything bad about Princeton in front of his son.
The younger Thompson fell in love with Princeton, married a woman from Princeton and bought a house next to the university, the father said.
Getting the head coaching job also proved to ba matter of being in the right place at the right time for John Thompson III, who has also served as the Princeton junior varsity coach the past four years.
Joe Scott, who was Carmody's top assistant, left after last season to coach Air Force, moving Thompson up the ladder.
Carmody, who had a 92-25 record in his four years as coach at Princeton, was introduced Wednesday at Northwestern. He was a Princeton assistant under Carril for 14 years.
Carmody replaces Kevin O'Neill, who resigned five days ago to become an assistant with the New York Knicks.
Matching the success of his father will be tough for Thompson.
The elder Thompson was inducted into the Basketball Hall of Fame last year and had 596-239 record before stepping down as Georgetown's coach on Jan. 8, 1999. The midseason move was made because the elder Thompson was going through a divorce and he felt he could not devote as much time as he wanted to basketball.
At Georgetown, Thompson guided the Hoyas to 20 NCAA tournaments, including 14 in a row, earned three Final Four berths and won the NCAA title in 1984. The 1988 U.S. Olympic coach, his teams had a 97 percent graduation rate and 26 players were taken in the NBA draft.
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