The 6-7 senior-to-be from Dallas will be counted on heavily next season with the departures of senior Markel Brown and sophomore Marcus Smart, who is entering the NBA Draft.
Nash averaged 13.9 points (third behind Smart and Brown) and 5.5 rebounds (second on the team to Kamari Murphy) last season as a junior.
Nash said after the Cowboys were eliminated from the NCAA Tournament last month that he was "50-50" on whether to return to OSU for his fourth and final season of eligibility.
He has started 89 of 95 games over the past three seasons, and is averaging 13.8 points and 4.9 rebounds during his career.
Nash had 24 double-figure scoring games this past season, including a career-high 29 points in OSU's 81-75 victory over West Virginia on Jan. 25, 2014.
Nash is just the third player since 1999 and just the ninth in school history to average double figures in scoring during his freshman (13.3), sophomore (14.0), and junior (13.9) seasons.