The 6-foot-1, 226-pound Gurley is the first running back taken in the first round since 2012.
The Rams opted to get backfield help for new quarterback Nick Foles instead of addressing a thin offensive line. Gurley is coming off knee surgery last November after being suspended for four games earlier in the season for a violation of NCAA rules.
Tre Mason, a third-round pick last year, led the Rams with 765 yards rushing and averaged 4.3 yards per carry.