SANTA CLARA, Calif. — The San Francisco 49ers signed free agent quarterback David Carr to a two-year deal Monday and agreed to terms with Detroit on a trade that would send backup quarterback Shaun Hill to the Lions for a 2011 draft pick.

Carr said he found San Francisco attractive since he is from California and there was a possibility of playing time after serving as Eli Manning's backup for the New York Giants the past two seasons.

49ers coach Mike Singletary has repeatedly said 2005 No. 1 pick Alex Smith is the starter, but didn't rule out signing an experienced quarterback who could push Smith and challenge for playing time.

"They have said that competition is what they love around here," Carr said. "It makes you feel better. One of Singletary's things is, 'Iron sharpens iron.' The thing that I wanted to hear, from all those guys, was I'll have a chance to be on the field if I play the way I know I can play and they said yes. Once I get on the field, I feel confident that we are going to play well."

Carr, an eight-year NFL veteran, was drafted No. 1 overall by the Houston Texans in 2002. He played right away for the expansion team and was sacked 76 times as a rookie.

In five seasons with the Texans, he completed 60 percent of his passes with 59 touchdowns and 65 interceptions for a quarterback rating of 75.5. He was also sacked 249 times in 76 games.

Carr then spent the 2007 season in Carolina where he made four starts and appeared in six games before backing up Manning the past two years.

"When I went to New York, I got around some awesome guys, awesome coaches that believed in me," Carr said. "They never showed a lack of confidence in me. That's why, when we went on the field, we had success. That stuff is important, but those last two years were great. I recharged my battery for my career and now I feel like my talent level, my experience level are right next to each other. Hopefully, that can transcend into helping the team win."

Smith took over for Hill at halftime Oct. 25 at Houston and started the rest of the way for San Francisco, which finished 8-8 and ended a franchise-worst stretch of six straight losing seasons.

Carr joined the team in time for the start of the voluntary offseason workout program and enjoyed spending time with Smith.

"It was fun to try to push each other, but he seems like a good guy," he said.

The 49ers would receive an undisclosed 2011 draft pick in return for Hill.