The deal calls for a $6.5 million salary next year and includes an $11.5 million mutual option for 2011 with a $1 million buyout. Harden can earn an additional $2.5 million next year in performance bonuses.
The oft-injured right-hander had to pass a physical before the agreement was finalized.
"When he's out there, this is a guy with No. 1 ability. He's a stopper in the true sense of the word. That's something we felt we needed," general manager Jon Daniels said on a conference call.
Texas reached a preliminary agreement with Harden on Wednesday, the same day it traded starting pitcher Kevin Millwood to the Baltimore Orioles along with $3 million for reliever Chris Ray and a player to be named.
Millwood is owed $12 million next year, so the deal freed up money for the Rangers to land Harden. The team had cash flow problems this year, with Major League Baseball stepping in to provide assistance, and owner Tom Hicks is trying to sell the team.
Daniels, however, said the topic of ownership came up very little during Texas' discussions at the winter meetings this week.
"It really was more about payroll and what we wanted to accomplish with the club under those parameters, regardless of the status of ownership," Daniels said. "It was more about, we could creatively figure out how to improve the club. We felt from this regard we had to move some pieces around to acquire somebody like Rich, and we're happy we did."
Harden struck out 171 batters in 141 innings last season, going 9-9 with a 4.09 ERA for the Chicago Cubs, who acquired him from the Oakland Athletics in July 2008 along with right-hander Chad Gaudin for right-hander Sean Gallagher, catcher Josh Donaldson and outfielders Matt Murton and Eric Patterson.
Harden, who turned 28 last month, is 50-29 with a 3.39 ERA in seven big league seasons. He has been slowed by seven trips to the disabled list for a strained left oblique (2005), strained back (2006 and 2009), sprained elbow ligament (2006), and strained shoulder (twice in 2007 and once in 2008).
Daniels declined to discuss the specifics of Harden's MRI exam. He said the Rangers were comfortable that the pitcher's previous injuries didn't involve deeper structural issues with his elbow or shoulder.
"We understand we're going to have to take some steps to keep him healthy," Daniels said. "We understand the risk involved."
Harden joins a rotation led by right-hander Scott Feldman, who went 17-8 with a 4.08 ERA last season.
"We like our chances with those two guys up there," Daniels said.
Harden can earn an additional $500,000 each next year for 155, 165, 175, 185 and 195 innings. He would get $250,000 if traded, and he has a limited no-trade clause.
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