Rudolph attended Elder High School in Cincinnati, Ohio, where he played high school football for the Panthers. As a junior, he caught 30 passes for 400 yards and seven touchdowns en route to earning first-team All-city and All-conference honors. As a senior in 2008, he was named first-team All-American by USA Today after totaling 37 receptions for 673 yards (18.2 yards per catch) and 11 touchdowns. He was placed on the Scout.com All-America first team and was the lone tight end among the 11 finalists for the high school Maxwell Award. He received first-team All-Southwest Ohio as a senior after being named second team as a junior and was named second-team All-state by the Associated Press. Following his senior season, Rudolph was invited to play in the 2008 U.S. Army All-American Bowl held in San Antonio, Texas.
As a freshman in 2008, Rudolph became the first tight end in Notre Dame history to start all 13 games as a freshman and the first freshman to ever start a season opener at tight end for Notre Dame. He made his career debut in the season opener against San Diego State and brought in his first career reception for five yards during the victory. In week 3, he posted his first multi-reception game (two catches for 29 yards) of his career against Michigan State, with both catches traveling for 10-plus yards and resulting in first downs against the Spartans. The following week, he hauled in three passes for 32 yards, with a long of 19, while also recording the first touchdown catch of his career in the Irish' 38-21 win over Purdue. In week 5, he registered season-highs in receptions (5) and receiving yards (70) and added his second and final touchdown of the season versus Stanford. He hauled in two catches for 26 yards against Pittsburgh, setting a new school record for receptions by a freshmen tight end in a single season during the game. In week 11, he established a school record for single-season receiving yards by a freshman tight end during the game against Syracuse. In the 2008 Hawaii Bowl game, he caught four passes for a season-high 78 yards. His 29-yard reception against the Warriors also set a season-best long reception. Rudolph finished his first year with the Irish with 29 receptions for 340 yards (11.7 avg.) and two touchdowns.