The six-time Super Bowl champion quarterback for New England joined Tampa Bay in March after 20 seasons with the Patriots.
Brady drove to the Bucs' headquarters and under protocols set by the league and NFL Players Association could only take his first virus test. He will take another in three days.
All players must return two negative COVID-19 tests before they are allowed to participate in other activities at team facilities, including an opening physical before workouts can commence.
Brady and other veterans are due to report for the start of training camp on Monday, a week before Brady's 43rd birthday.
Negotiations continue between the NFL and the union regarding the upcoming season, scheduled to begin September 10 with the reigning champion Kansas City Chiefs playing host to Houston.