The right-hander will make a base salary of $650,000 with another $100,000 possible through games-started incentives.
Benson threw a simulated game against Arizona Minor Leaguers last week.
"He was 88-89 [mph] the other day, he can sink the ball pretty well now. He's got four pitches, good command," D-backs GM Josh Byrnes said. "Like any pitcher, the more he's out there, the better his stuff is going to get. He's reinvented himself a little bit but he's still got plenty of stuff to give himself a chance."
Benson was the first overall pick in the 1996 First-Year Player Draft. Initially selected by the Pirates, Benson has also pitched for the Mets, Orioles and Rangers in parts of eight seasons.
"Probably the tricky thing is the quality of his resume, [being the] first pick in the Draft, [he's had] a good career, but also understands here and now where he fits," Byrnes said. "He's got to come in and compete and ultimately outperform people in order to get a shot, but he embraced the opportunity and we're glad to have him."
Benson had rotator cuff surgery in 2007 and did not pitch in the big leagues that year or in '08. Last season, he was 1-1 with an 8.46 ERA in eight games (two starts) for the Rangers.
Getting a look at Benson this spring in big league games will be somewhat challenging, but the fact that he has already built up his arm strength will help him.
"We probably have at least one [Major League] game earmarked that we can give him," Byrnes said. "He's already progressed out to five innings, 80-85 pitches. I think we'll probably get him into one Major League game possibly more between now and Opening Day."
Right-hander Brandon Webb will start the season on the disabled list, but Byrnes said signing Benson was more a product of the team adding to its inventory of starting pitchers rather than as a replacement for Webb.
"Any attempt to improve our depth we feel is worth doing," Byrnes said.
Steve Gilbert is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.