House attended Arizona State University in Tempe, Arizona. His college basketball career was marred by implication in one of the worst point shaving scandals in sports history as a freshman, when teammates Stevin Smith and Isaac Burton were bribed by former campus bookmaker Benny Silman to ensure the Sun Devils did not cover the alotted spread in four end of season basketball games during the 1994 season.
After overcoming the obstacles placed in front of him, where Arizona State could not recruit a supporting cast, House became the all-time scoring leader at Arizona State with 2,044 points in his career and the is the only player to score more than 2,000. Along with Ike Diogu, they are the only two former Sun Devils to have been named Pac-10 Player of the Year and Eddie House is the fifth Sun Devil to be voted onto the All-Conference team twice. He is also the career record holder at Arizona State for field goals and steals. He set the single-season scoring average record for the school with 23.0 points per game in 1999-2000. In that season he was named Pac-10 Player of the Week a record-tying four times (accomplished only by Ed O'Bannon, Chris Mills, and Gary Payton). House's single-game Arizona State record 61-point effort in a double-overtime against the University of California Golden Bears on the road in his senior season Bay Area homecoming is arguably the most memorable single-game performance of any player in the Pac-10 since the University joined the league in 1978. In that game House also set a record with 18 made free throws in 19 attempts. He is one of only three players to average in double figures in four consecutive seasons at Arizona State since it joined the Pac-10.
On November 18, 2005, he scored a career-high 31 points against the Utah Jazz.