The deal announced Thursday contract $250,000 in performance bonuses.
Paulino opened the season on the disabled list because of a strained forearm, then went 3-1 with a 1.67 ERA in seven starts before tearing a ligament in his right elbow.
He underwent ligament-replacement surgery, spent the rest of the summer rehabbing and is expected to be ready to pitch again sometime during the middle of next season.
The only remaining Royals players eligible for arbitration are second baseman Chris Getz, who made $967,500 last season, and right-hander Luke Hochevar, who made $3.51 million. The deadline to offer contracts to unsigned players on 40-man rosters is Friday.