A source says Andrus' deal, which is pending a physical, is worth between $14-15 million.
Andrus, 23, will avoid arbitration for the remainder of his career with Texas thanks to the contract. He batted .279 with five homers and 60 RBIs with 37 stolen bases in 2011.
It was Andrus' third season in the league as the club's starting shortstop. He was second in the AL rookie of the year balloting in 2009, hitting .267 with six homers and 40 RBIs with 33 stolen bases. He had a .265 average with no homers and 35 RBIs with 32 stolen bases in 2010.
Andrus was acquired as part of the Mark Teixeira trade in July 2007 and never even played in Triple-A before earning the starting shortstop spot in 2009. Michael Young, who was a Gold Glove shortstop in 2008, moved over to third base to accommodate Andrus' arrival.
Cruz, whose eight postseason homers last year included six in the AL Championship Series with a game-ending grand slam in Game 2, asked for $7.5 million while the Rangers offered $5.5 million. He made $3.65 million last year, when he hit .263 with 29 homers and 87 RBIs in 124 games.
Napoli set career highs by hitting .320 with 30 homers and 75 RBIs in 113 games in his first season with Texas, when he made $5.8 million after spending his first five seasons with the Los Angeles Angels. He asked for $11.5 million, and Texas offered $8.3 million.
Richard Durrett covers the Rangers for ESPNDallas.com. Information from The Associated Press was used in this report.