Price, who was the 21st overall selection of the 2018 NFL Draft, partially tore his pectoral muscle while doing the bench press at the NFL Scouting Combine in March.
"Fully cleared for football again," Price tweeted on Monday morning.
Fully cleared for football again 🙌🏼— Billy Price (@b_price53) June 18, 2018
Price has been limited in offseason practices because of the injury. He is expected to start at center this season on a revamped offensive line for the Bengals, who open training camp on July 26.
The 6-foot-4, 305-pound Price started at guard for three seasons with Ohio State before shuffling to center in 2017.
Price is the 2017 Big Ten Rimington-Pace winner as the conference's top offensive lineman and Rimington Trophy winner as college football's top center. He finished his career with school records for both total and consecutive starts (55).
Price was also an All-American at left guard in 2016 before earning the same honors in 2017 as a center.