“I am ready for the journey and anxious to get back to work as we prepare to win another national championship,” Arnette wrote.
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Arnette had 40 tackles, an interception and six pass breakups last season.
He has started 25 games over the last two years as Ohio State has generally deployed a three-man rotation at cornerback.
He had 44 tackles and two interceptions with eight PBUs in 2017.
Receiver K.J. Hill announced Tuesday he will return while quarterback Dwayne Haskins, center Michael Jordan, running back Mike Weber and defensive linemen Nick Bosa and Dre'Mont Jones have declared they will enter the draft.
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Also coming back is Jordan Fuller, a two-year starter at safety who made his announcement last week.
Arnette and Fuller were part of an Ohio State secondary that struggled much of the season and will be under new management in 2019.
Jeff Hafley has been hired as co-defensive coordinator and secondary coach. He spent the past six seasons in the NFL.