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O'Day, 28, was arbitration eligible, but an agreement was reached shortly after the two sides exchanged figures and discovered there was not much of a gap between them.
O'Day, who was acquired off waivers in 2009, appeared in 72 games with the Rangers last season, logging 62 innings with a 2.03 ERA.
Josh Hamilton and Frank Francisco are the Rangers' two remaining arbitration-eligible players that have yet to come to an agreement. The two sides have until hearing dates in mid-February to reach a deal.
Richard Durrett covers the Rangers for ESPNDallas.com. You can follow him on Twitter or leave a question for his mailbag.