The three individuals are joined by Burnley assistant manager Ian Woan, while the other two individuals are at a third club but the details have not been revealed.
Those who have tested positive will now have to self-isolate for seven days.
In total, 748 players and staff were tested from 19 clubs, while Norwich City completed their tests yesterday (19.05.20).
Burnley confirmed Woan was "asymptomatic" and "currently safe and well at home".
The club said in a statement: "He will remain in close communication with club personnel regarding his re-engagement in training once he is clear of the virus."
While Watford confirmed a player and two staff members had tested positive, the club won't be naming the three individuals as they requested medical confidentiality.
Manager Nigel Pearson had previously said he wouldn't insist on players reporting for training, and captain Troy Deeney confirmed he wouldn't be returning over concerns for his family's health.
He said: "It only takes one person to get infected within the group and I don't want to be bringing that home.
"My son is only five months old. He had breathing difficulties, so I don't want to come home to put him in more danger."