According to sources, the deal is worth $9.4 million.
The agreement allows both sides to avoid a hearing, which was scheduled for Wednesday.
Napoli's deal means Texas will continue its streak of not going to any arbitration hearings since 2000 (Lee Stevens). The Rangers also completed deals this week with slugging outfielder Nelson Cruz and shortstop Elvis Andrus to avoid hearings. Cruz and Andrus got multiyear deals that took them through their last arbitration-eligible seasons, Cruz through 2013 and Andrus through 2014.
Napoli's contract represents a $3.6 million raise from his 2011 salary ($5.8 million). He earned it after putting up a career-high .320 average with 30 homers and 75 RBIs in 113 games for the Rangers last season. Napoli, 30, who was acquired in a trade with the Toronto Blue Jays last January for reliever Frank Francisco, settled $500,000 below the midpoint after the sides exchanged figures. Napoli asked for $11.5 million and the club offered $8.3 million.
Napoli earned more playing time as the season progressed, batting .383 with 18 homers and 42 RBIs after the All-Star break. He likely would have been the World Series MVP had the Rangers won after batting .350 with two homers and 10 RBIs.
The 30-year-old Napoli is a .264 career hitter with 122 homers and 324 RBIs in 619 games.
Napoli said his left ankle, which was injured as he tried to round second base on an errant throw in Game 6 of the World Series, is feeling better. He's been able to participate in his offseason workouts and said recently that he will be fully ready for spring training.
Richard Durrett covers the Rangers for ESPNDallas.com. Information from The Associated Press was used in this report.