The team scheduled a Wednesday morning news conference to announce the deal, the source said, speaking on condition of anonymity.
Vick, considered one of the most exciting quarterbacks to come out of college in years, will be in Atlanta to sign the contract Wednesday, said the source, who would not disclose financial terms.
One of Vick’s agents, Mike Sullivan, was en route to Atlanta and did not immediately return a phone call for comment.
ESPN.com reported that Vick would sign a six-year contract worth up to $62 million.
He will receive an initial signing bonus of $3 million and is guaranteed $15.3 million over the first three years, the Web site reported.
The Falcons, who have a 9-23 record since an improbable run to the 1999 Super Bowl, landed the top draft pick in a trade with the San Diego Chargers the day before the draft.
Atlanta gave up three draft picks and receiver-returner Tim Dwight to get Vick, who played just two years at Virginia Tech before turning pro.
Atlanta coach Dan Reeves has made it clear that veteran Chris Chandler will remain the No. 1 quarterback, but the coach also stressed that he plans to get Vick into the lineup as soon as possible.
At a rookie mini-camp last weekend, Vick ran the 40-yard dash in 4.36 seconds, the fastest time among the 19 draft picks and college free agents at the mandatory camp.
He later sat out some drills with an upset stomach, which he attributed to overeating at lunch.
As a redshirt freshman, Vick led Division I-A in passing efficiency and finished third in the Heisman Trophy voting.
In one of his best performances, he passed for 225 yards and ran for 97 more against Florida State in the 2000 championship game, which the Hokies lost 46-29.
Last season, Virginia Tech’s hopes were hampered by Vick’s severely sprained right ankle.
But he finished his career with a solid performance in a 41-20 victory over Clemson in the Gator Bowl