Details of the deal were not available.
Carter has been in the league 11 years since being drafted out of California by the San Francisco 49ers in 2001.
He spent five seasons with the Niners before joining the Washington Redskins where he has played since 2006.
Carter amassed 44 tackles (25 solo) and 2.5 sacks last year in Washington.
At 6-foot-4, 257 pounds, Carter projects best to defensive end in a more traditional four-man line.
The Patriots have been utilizing a four-man line through the first stretch of training camp, with Eric Moore and Jermaine Cunningham the top ends. In the last three days, the team has added three new players to the mix -- Mark Anderson, Shaun Ellis and now Carter.
Carter, who has 66 career sacks, totaled 11 in the 2009 season. He has played in 149 career regular-season games, with 133 starts.
Source: Falcons keep Snelling
Snelling, the top backup to Michael Turner, had been testing the market as a restricted free agent.
He could be challenged a bit for playing time this year by fifth-round draft choice Jacquizz Rodgers.
The 5-foot-11, 223-pound back rushed for 324 yards and two touchdowns last season and a total of 613 yards and four touchdowns in 2009.
Snelling also has a total of 74 receptions and four touchdown catches in the past two seasons.
Bradford looks sharp
Rams quarterback Sam Bradford looked sharp executing the new St. Louis offense in the red zone Sunday during the scrimmage at Lindenwood University.
Bradford completed 13 of 20 passes for 140 yards and four touchdowns against the second-team defense. He had one interception. All the touchdowns came during red-zone work.
Bradford's favorite target was Danny Amendola, who caught eight passes for 70 yards. Mike Sims-Walker caught three passes for 71 yards and a touchdown. He had an over-the-shoulder catch, good for 21 yards.
The scrimmage involved running plays, third-down situations and red-zone work before an estimated crowd of 6,200 at Harlen C. Hunter Stadium. The temperature reached 94 degrees with a heat index of 108.
Texans sign LB Dobbins
The 6-foot-1, 246-pound Dobbins was a fifth-round pick by San Diego in 2006. He played four seasons with the Chargers before he was traded to Miami during the 2010 draft. He was cut by the Dolphins on Monday.
Dobbins has played in 78 games with 16 starts. He has 196 tackles, two sacks, two interceptions and four forced fumbles. He played in all 16 games last season, including six starts. He finished with 43 tackles and a sack.
Information from The Associated Press was used in this report.