Bloomgren, 40, has been at Stanford since 2011, coaching the offensive line for the past seven seasons and serving as offensive coordinator since 2013.
Bloomgren will replace David Bailiff, fired Nov. 27 after 11 seasons at the school. Before coming to Stanford, Bloomgren spent four seasons coaching with the New York Jets.
Rice also considered South Carolina offensive coordinator Kurt Roper and Stanford defensive coordinator Lance Anderson in its coaching search.
Yahoo! Sports first reported the decision.