The contract is for one year and $1 million with incentives that could increase the overall value of the deal.
The presence of Giants assistant coach Chris Palmer, who worked with Carr in Houston, was a major reason the quarterback chose New York.
"Chris knows me better than anybody," Carr told ESPN.com. "I'm looking forward to getting in there and working with him on what's right and wrong with my mechanics."
Carr, 28, spent last season with Carolina and struggled after taking over for an injured Jake Delhomme. Carr was the No. 1 overall pick in 2002 by Houston and spent the first five years of his career there.
He is expected to compete for the backup job behind Eli Manning.
"I have a lot of calluses," Carr said, according to The Associated Press. "I'm like an old carpenter I've been through it. If you let that stuff affect you, you're not going to be able to do your job. One of the reasons I'm excited about coming here is they protect the quarterback well and they have playmakers on the outside."
Taken first by Houston in the 2002 draft, Carr has seen his career falter in recent seasons. He was released by the Texans after the 2006 season and signed a two-year, $6 million deal last year with the Panthers.
The Panthers released him after this past season.
Carr had a 58.3 passer rating with just three touchdown passes and five interceptions after replacing the injured Delhomme. Carr was eventually replaced by 44-year-old Vinny Testaverde and then undrafted rookie Matt Moore.
The Fresno State product has played in 82 career games with 79 starts. He started all 16 games four times in his five seasons with the Texans, including the last three.
Careerwise, Carr has completed 1,316 of 2,206 passes for 14,026 yards, 62 touchdowns and 70 interceptions. His career passer rating is 74.4. He has been sacked 262 times, including a record 76 for 411 yards in losses as a rookie in '04.
"I think any player coming into a situation like this has to prove something," Carr said. "I have to work just as hard or harder than the guys there. They've been to the top. They won a Super Bowl. They don't need our help."
Giants coach Tom Coughlin called Carr a talented, athletic player.
"We look forward to working with him on the fundamentals of the game," Coughlin said. "We do have some technical things to work on, but we are anxious to work with him in our program. If we can place him in a positive environment, perhaps he can reclaim some of the things that people saw to draft him in the first round."
Carr had career-high totals of 54 passes and 39 completions in Giants Stadium against the Jets on Nov. 26, 2006. He tied the NFL single-game record with 22 consecutive completions versus Buffalo on Nov. 19, 2006. Carr has passed for more than 300 yards four times, including a career-high 372 against Minnesota on Oct. 10, 2004. He has directed 11 career game-winning drives in which the decisive points were scored in the fourth quarter or overtime, including one last Oct. 7 in New Orleans.
Carr's best season came in 2004 when he passed for 3,531 yards and 16 touchdowns. Although he had 14 interceptions, the Texans finished 7-9, the best season at that point in the franchise's first three seasons.
But the Texans regressed to 2-14 the next season and 6-10 in 2006. The Texans then acquired former Falcons backup Matt Schaub and cut loose Carr for 2007. With Schaub and then Sage Rosenfels -- who took over due to injury -- at the helm, the Texans went 8-8.
Pat Yasinskas covers the NFL for ESPN.com. Information from The Associated Press was used in this report.