Ross, the ninth overall pick out of Washington, joined fourth-round defensive end Carl Lawson as the first two of the team's 11 draft picks to sign.
Drafted players get four-year deals with a team option for a fifth season.
The Bengals broke their rookie minicamp following a Sunday morning practice.
"It's great for John that this part of it is out of the way," Bengals head coach Marvin Lewis said in a statement. "This gives him the opportunity to focus on finishing school and then football and I think that's important."
The 5-foot-11, 190-pound Ross, who ran a 40-yard dash in a record 4.22 seconds at the NFL Scouting Combine in March, won't return to Cincinnati until after his June 10 graduation per league rules.
Ross' family plans to travel for the graduation.
"Emotional for my family," Ross, who will receive a degree in American Ethnic Studies, told the team's website. "The biggest thing is just to see how happy my family is. That's really the biggest part. When I see them. I'm the first generation to go to a university and just to see how happy it's going to make my mom and my grandmothers."
In 2016 at Washington, Ross had 81 catches for 1,150 yards and 17 touchdowns.
The 6-2, 253-pound Lawson, the Bengals' first pick in the fourth round out of Auburn, is an edge rusher who recovered from two injury-riddled seasons to register 12.5 tackles for losses, including nine sacks, and an All-SEC first-team berth.