The decision marks a major step forward for the Premier League's much-discussed Project Restart plans, which are geared towards playing behind-closed-doors games later in the summer to complete the 2019/20 league season.
As a result of the vote, squads are now able to train as a group and engage in tackling - though they must still maintain social distancing.
In a statement, the Premier League explained: "The Premier League's priority is the health and wellbeing of all participants.
"Strict medical protocols are in place to ensure the training ground is the safest environment possible and players and staff will continue to be tested for COVID-19 twice a week.
"Stage Two of the Return to Training protocol has been agreed following consultation with clubs, players, managers, the PFA, LMA and the Government.
"Discussions are ongoing as work continues towards resuming the season, when conditions allow. (sic)"
Meanwhile, Liverpool boss Jurgen Klopp recently insisted "it is safe" to resume the Premier League campaign.
Speaking to club media, he said: "Nobody wants to bring anybody into danger, but I think with all the things we know about, the players will be safe.
"With testing as often as possible Germany showed it already. They had 10 or 12 positive tests, and now they play already.
"That shows we [can] create a 'society' in which we really make sure nothing will happen. That football is closer to coming back I think is really a good sign for people as well."