Both contracts for the pitchers are one-year deals. Webb's deal includes up to $5 million in incentives with a $3 million base. Rhodes' is for $3.9 million with a vesting club option for $4 million in 2012.
Webb, 31, is returning following shoulder debridement surgery in August 2009 to clean out loose debris and inflamed tissue. The surgery was performed by Rangers physician Keith Meister.
Webb has pitched just four innings the last two years but is expected to be fully healthy for spring training. He pitched in the instructional league in October.
"I feel good right now, feel good where I'm at," said Webb, who threw four innings over 1½ weeks in instructional league. "I felt comfortable on the mound each time I went out there. My velocity got better and my stuff got better. Just taking it from there, I feel like I'm going to be ready for spring training for sure."
General manager Jon Daniels said the Rangers were encouraged by how Webb felt and that Meister felt the pitcher "was where he should have been from a conditioning standpoint. ... All of the checkpoints you'd look at were there."
Webb won the Cy Young Award in 2006 and was an All-Star the two seasons after that. In his last full season, 2008, Webb had 22 wins.
The right-hander joins the American League champions, who continue to try to bolster a pitching staff that will be without Cliff Lee, who signed with the Philadelphia Phillies last month. Webb becomes a member of the starting rotation that includes left-hander C.J. Wilson, who won 15 games in 2010, and Colby Lewis, who beat the Yankees twice in the ALCS.
Tommy Hunter, Derek Holland and left-hander Michael Kirkman will also get a shot at the rotation along with closer Neftali Feliz, who will head to spring training stretched out so the club can decide whether he becomes a member of the rotation. Feliz was the AL Rookie of the Year in 2010 after saving 40 games.
Rhodes, 41, is coming off his first All-Star season with Cincinnati. He had 69 appearances, his most since 2001, and a 2.29 ERA in 55 innings. He gives the Rangers another veteran left-handed presence in the bullpen (joining 40-year-old Darren Oliver).
"It feels great to be a Ranger right now," said Rhodes, who was born in Waco, about 100 miles from Rangers Ballpark, though he currently lives in Maryland. "I'm feeling good and read to go."
In conjunction with Webb's arrival in Texas, sources told ESPN.com's Jerry Crasnick that the pitcher has asked to wear uniform No. 33 as a tribute to his late friend, college roommate and baseball teammate, Jon Hooker. Webb previously wore uniform No. 17 with the Arizona Diamondbacks.
Hooker, who played with Webb and Joe Blanton at the University of Kentucky, died in a plane crash a day after his wedding in August 2006. Hooker and his wife, Scarlett, were on the first leg of a trip from Lexington, Ky., to their honeymoon in California when their plane crashed and burst into flames. All 47 passengers and two of the three crew members aboard the Comair commuter jet were killed in the accident.