Speaking with reporters before the Ohio State Football Job Fair in Columbus, Meyer named Haskins the starter but said sophomore Tate Martell will compete for the top job when practices resume later this summer.
Haskins, Martell and Joe Burrow competed during spring practice, but Burrow last month left the team to join LSU as a graduate transfer.
The 6-foot-3, 218-pound Haskins appeared in eight games last season, completing 40 of 57 pass attempts for 565 yards with four touchdowns and one interception. He relieved injured starter J.T. Barrett in Ohio State's win at Michigan, completing 6 of 7 pass attempts for 94 yards.
ESPN rated Haskins as the No. 4 pocket passer and No. 63 overall player in the 2016 recruiting class. Martell rated as the No. 6 dual-threat quarterback and No. 127 overall player in the 2017 class.