The bill passed by the Senate Thursday also provides an additional five years for prosecution from the time a potential suspect is identified through DNA testing.
The legislation comes as the Attorney General's Office continues to plow through a backlog of untested rape kits, with numerous cases of DNA matches in a criminal database.
The Ohio House approved a similar bill last month.
Opponents have told lawmakers they believe the bill is unconstitutional because it creates two classes of offenders — those whose cases involve DNA evidence, and those whose cases don't.