The Falcons later confirmed that Konz had signed his contract.
Konz was taken in the second round (No. 55 overall). His deal is worth $3.588 million over four years and includes a $1.05 million signing bonus, according to the website.
The 6-foot-5, 314-pound Konz played center at Wisconsin but is expected to compete for a starting spot at guard.
The Wisconsin native said Saturday he was adjusting to the southern heat during rookie minicamp, joking that he wanted an air conditioner in his helmet.
The Falcons also signed three other draft picks to contracts Sunday: Wisconsin fullback Bradie Ewing (fifth round), Mississippi State safety Charles Mitchell (sixth) and South Carolina defensive tackle Travian Robertson (seventh). Two of the team's six picks, Southern Mississippi offensive lineman Lamar Holmes (third) and Georgia defensive end Jonathan Massaquoi (fifth), remain unsigned