He is the first Rutgers player drafted since guard Quincy Douby was selected 19th overall in the 2006 NBA draft.
"I have come a long way, but I still have further to go," Ndiaye said. "I would like to thank the Timberwolves for this tremendous opportunity. I would also like to thank my family, my friends and the good people at Rutgers University for all of their support.
"Playing in the NBA has been a dream. Now that it's within reach, I am going to do whatever it takes to make it come true."
Ndiaye averaged 9.4 points, 7.1 rebounds and 4.5 blocks per game as a senior, and was the Big East's Defensive Player of the Year. He finished his career with 358 career blocks, three more than the mark Roy Hinson held for decades.