The Illini (36-1), who play Louisville in the national semifinals Saturday, were ranked No. 1 the final 15 weeks of the season, and were unanimous six times.
Only two other Illinois teams, in 1953 and 1989, were ever ranked No. 1, and both also reached the Final Four, but neither lasted on top more than a week during the season.
Weber received 54 votes from the 72-member national media panel that selects the weekly AP Top 25.
Mike Krzyzewski of Duke received six votes, while Al Skinner of Boston College had five and Lorenzo Romar of Washington had four.
Weber succeeded Bill Self at Illinois two years ago and led the Illini to their first outright Big Ten title in 52 years in his first season.
Weber coached Southern Illinois for five seasons, compiling a 103-54 record and leading the Salukis to the NCAA tournament twice, before the Illinois job opened when Self moved to Kansas. Weber was an assistant for 18 seasons to Purdue's Gene Keady, the coach of the year in 1996.
Weber's 81-year-old mother, Dawn, died suddenly the day the Illini beat Northwestern in the quarterfinals of the Big Ten tournament. He didn't miss a game as Illinois went on to win the conference title and then won four games as the NCAA tournament's overall No. 1 seed. The Illini reached the Final Four with a memorable 90-89 overtime victory over Arizona, a game in which they trailed by 15 with 4 minutes left in regulation.
Weber is the first Illinois coach to win the award and the first from the Big Ten since Tom Izzo of Michigan State in 1998. Izzo's Spartans also reached the Final Four this season, setting up the possibility of an all-Big Ten national championship game.
Phil Martelli of Saint Joseph's won the award last season.
Story provided by the University of Illinois press release.