"He proved to me he could be a head coach in his audition," Alleva said.
Roof was 2-3 as interim coach after Carl Franks was fired Oct. 19, breaking the program's 30-game conference losing streak with a victory over Georgia Tech and a 13-game skid against rival North Carolina. Two of the losses were close games against Tennessee and North Carolina State.
"I've known what I've wanted to do since I was 17 years old," said Roof, a former Georgia Tech linebacker. "I wanted to be a head football coach in the Atlantic Coast Conference. There has been no other goal."
Since going to their last bowl in 1994, the Blue Devils have a combined record of 18-83, including three 0-11 seasons.
"We have a great university to sell, not just in the state of North Carolina but all over America," Roof said. "When you think of Duke you think of excellence and respect.
"So, we're going to go after the best athletes in America that can compete on the field for us and in the classroom. We will go from the North Pole to the South Pole to find them and to educate them about Duke."
The players endorsed the 39-year-old coach for the full-time job one week after he took over for Franks.
"What the players said to me had absolutely nothing to do with my decision -- zero," Alleva said. "What the players did on the field had something to do with it."
Quarterback Chris Dapolito said the team meeting with Roof on Saturday was upbeat.
"We got a little sample of what coach Roof could do for five weeks," Dapolito said. " We're excited to see what he can do for a whole year."