Yates replaces John Gregory, who stepped down to have heart surgery in December and then announced he would not be returning earlier this month.
Dean Saunders took over as interim boss but was unable to save Crawley from relegation to Sky Bet League Two and has since moved to Chesterfield.
Yates, 45, who has agreed a two-year contract, parted company with the Robins in November after almost five years in charge. He was the third longest-serving manager in the league at the time of his departure.
“I’m delighted to be here,” Yates told Town’s official website. “I have been out of the game for a few months and when this opportunity came up it really excited me. There’s a big challenge ahead but one I am really looking forward to.”
Chief executive Michael Dunford said: “We’re delighted that Mark has agreed to join us. We interviewed some very strong candidates but Mark stood out.
“He has a very deep knowledge of the level we find ourselves at next season and is a first-rate coach.
“The board spoke to several people in the game who have worked with Mark and they were all very positive about his credentials, his knowledge and his enthusiasm and we are looking forward to Mark taking the club forward.”