The Giants gave up a 2011 fifth-round draft pick and a conditional 2012 selection based on how much Rosenfels plays.
They also received running back/kick returner Darius Reynaud in the deal. New York has been seeking a kick returner since Domenik Hixon suffered a season-ending knee injury during an offseason practice.
"We felt like we could better ourselves with the future considerations involved in the trade," Vikings coach Brad Childress said in a text message to the Minneapolis Star Tribune. "Obviously, the Giants had a need and we feel like we have two able-bodied guys behind Brett (Favre) right now."
Rosenfels, 32, most likely will supplant second-year pro Rhett Bomar as the Giants' No. 2 quarterback. New York signed Jim Sorgi as a free agent this offseason, but the veteran backup went on season-ending injured reserve earlier this week because of a shoulder problem, opening the door for the trade for Rosenfels.
"I'm excited," Rosenfels told the Star Tribune. "It's one of the traditionally best teams in the NFL, so that's exciting, and to get a chance to work with Eli [Manning]. He won a Super Bowl, and it's one of the greatest cities in the world. It's definitely one of my favorite cities, so that's an added bonus."
At the time, Rosenfels was thrilled to have a legitimate shot at winning a starting job for the first time in his NFL career. But after an offseason of working out and learning the system, Rosenfels' big dream was dashed when Favre waltzed in to take over the position.
There was a brief glimmer of hope for Rosenfels this summer while Favre considered retirement. Once again, that ended after the first preseason game, when the Vikings flew three high-profile teammates to Mississippi to persuade Favre to return for one more year.
Time was running out for Rosenfels, who grew more frustrated with his position on the team, although he was complimentary of the Vikings while departing for New York.
"I learned a ton from (offensive coordinator) Darrell Bevell and (quarterbacks coach) Kevin Rogers. Stuff that I'll try to carry onto anything I can help Eli with or those coaches with," Rosenfels told the Star Tribune. "Obviously, playing with Brett was a once-in-a-lifetime experience that I'll cherish forever. ... But I'm excited about this opportunity."
Rosenfels had an impressive preseason opener at St. Louis, completing 23 of 34 passes for 310 yards and three touchdowns. But he was just 8 of 17 for 92 yards with one touchdown in the next three games combined, and Vikings coach Brad Childress said after the preseason finale that Jackson would be Favre's backup again this season.
"I think you go into every opportunity with high expectations and high hopes," Rosenfels said when asked if he regretted that things didn't work out in Minnesota. "I feel like I put all of my energy into having as much success as I could have and this team could have over the course of the last year and a half. I have no regrets about how I approached coming to work every day. I have the utmost respect for those guys on that team."
Rosenfels has played in 32 NFL games with the Miami Dolphins and the Texans and thrown for 4,156 yards and 30 touchdowns with 20 interceptions. He was a fourth-round pick by the Washington Redskins in the 2001 draft, but he never played in a regular-season game with the team.
Bomar, 25, has played well in the preseason, but he hasn't seen any regular-season action in his career.
The Associated Press contributed to this report.