Teixeira hit .301 with 43 home runs and 144 RBI last season. The RBI were the most for a switch-hitter, breaking the record set by George Davis, who had 136 RBI for the New York Giants in 1896.
The Rangers also agreed to one-year deals with right-hander Adam Eaton ($4.65 million) and outfielder Brad Wilkerson ($3.9 million), avoiding arbitration with two players acquired in separate trades last month.
Teixeira will get $6 million this season and $9.4 million in 2007. He will turn 26 in April and is not eligible for free agency until after the 2008 season.
"It's pretty exciting not to have this to be a topic of conversation the next couple of years," manager Buck Showalter said.
"He's a pretty special person, a pretty special player, in that order," Showalter said. "When I go over a list to be concerned with, Mark being ready and being as good as he can be is not one."
Wilkerson, expected to be the Rangers' leadoff hitter, came over from the Nationals in the deal that sent All-Star second baseman Alfonso Soriano to Washington. Wilkerson would earn $50,000 bonuses for playing in 135 and 150 games. He hit .248 with 42 doubles, 11 homers, 57 RBI and 84 walks in 148 games last season.
Eaton was part of a six-player trade with the San Diego Padres. He was 11-5 with a 4.27 ERA last season, when he was limited to 128 2/3 innings and 24 games (22 starts) because of a strained middle finger.
Three Texas players remained eligible for arbitration: Pitcher Vicente Padilla (who asked for $4.8 million and was offered $4.1 million) and outfielders Gary Matthews Jr. ($3 million and $2 million) and Kevin Mench ($3.05 million and $2.45 million). The Rangers haven't had an arbitration case go to a hearing since 2000.
In three major-league seasons, Teixeira has a .282 career average with 107 homers and 340 RBI. The former first-round pick was among 42 players selected Monday for the initial U.S. roster for the World Baseball Classic.
Teixeira also won a Gold Glove last season, when he led AL first basemen with a .998 fielding percentage, making three errors in 1,483 chances. He started all 162 games, 154 at first and the rest as the designated hitter.
"Mark is an integral part of what we are trying to do here," general manager Jon Daniels said. "He's the kind of person and player we want to build around."
Texas selected Teixeira fifth overall in the 2001 amateur draft and gave him a $9.5 million, four-year contract.
Teixeira opted to attend Georgia Tech after being drafted by Boston in the ninth round in 1998. Three years later, after he played in just 16 games his junior season because of a broken right ankle, Texas drafted him.
Even though he was limited by an elbow injury to just 86 minor-league games, and none above the Double-A level, Teixeira broke spring training with the Rangers in 2003.
Teixeira was a third baseman in college. He adapted so quickly to the switch to first base that he took over as the Rangers' primary first baseman as a rookie, while Rafael Palmeiro was mostly a designated hitter in his last season in Texas.
"One of the things I love about Mark, Mark attacks his weaknesses," Showalter said. "He turned himself into a Gold Glove first baseman. A lot of people would have used the position change as an excuse. He's very driven, a self-starter."