Coach Bronco Mendenhall made the announcement Friday after both quarterbacks essentially played evenly throughout fall camp. Nelson, a junior, is expected to start the season opener Sept. 4 against Washington, but Heaps also will play.
"Each is a talented player with a different style, which will pose some difficulties for opposing defenses. Both players are committed to this decision and excited to lead our team," Mendenhall said in a statement released through the school.
Nelson and Heaps have been in a heated quarterback competition since the spring to replace the departed Max Hall, who became the all-time Mountain West career passing leader last season, and is BYU's career wins leader with 32.
Heaps, a true freshman from suburban Seattle, enrolled in school early and was able to take part in spring practice. One of the most highly touted quarterback prospects to go to BYU, he impressed with his arm strength and poise. In high school, he led his team to three straight championships while going 40-2.
Nelson served as Hall's backup last season, going 7-of-10 for 99 yards and one touchdown while running for 122 yards and three touchdowns. He started eight games as a freshman at Utah State in 2006 before leaving for a mission and transferring to BYU.
"I know this will give us an opportunity to have a highly successful season," Nelson said in the statement. "Jake and I both have the ability to lead our team and offer unique skills that will help us be successful as an offensive unit. I am excited about this opportunity and fully expect that we will carry on the great tradition and legacy of the quarterback position here at BYU."
Added Heaps: "I am 100 percent behind this decision. I feel the coaches have made the right decision for both Riley and I and this football team. Riley is a great player and I'm excited to have the opportunity to contribute. This isn't about me or him; it's about us -- it's about doing what we can to help our team."
Andrea Adelson is a national college football blogger for ESPN.com.