Saints were punted from the match that decides who joins England's lucrative top tier, after admitting to spying on semi-final opponents Middlesbrough.
Southampton have also been docked four points, to take effect from the start of next season.
Middlesbrough are now set to take on Hull in Saturday's play-off final at Wembley, pending a successful appeal from Southampton.
It is a stunning turn of events for attacker McGree, who otherwise would likely already be in the Socceroos' pre-World Cup training camp in Sarasota, given a large contingent of Championship players headed to the US once their seasons ended.
Instead, McGree, who scored in the second leg of the heartbreaking semi-final loss to Southampton, will have to put World Cup thoughts on hold and turn his attention to the biggest game of his club career.
Silvera hasn't been used in recent weeks after time out with an ankle injury, but had played a crucial role for Boro earlier in the season and could yet be called into camp.
Prior to the goalless first leg of their May 9 play-off semi-final, Â Middlesbrough reported to the EFL that a member of Southampton staff had spied on a training session on May 7, in breach of league rules.
The EFL charged them the following day. Southampton went on to win the semi-final 2-1 on aggregate after extra time in the second leg, after McGree had scored the first goal.
Southampton will appeal the sanctions, laid down by an independent commission, which heard the case on Tuesday.
The EFL said the parties were working to ensure an appeal is heard on Wednesday.
"Subject to the outcome, it could result in a further change to Saturday's fixture," the EFL said.
Hull City are also believed to be considering legal action.
The EFL confirmed further charges had been laid against Southampton on Sunday, and that Southampton had admitted observing training sessions ahead of matches against Oxford last December and Ipswich in April 2026, as well as the one before the Boro game.
The EFL said the written reasons for the commission's sanctions would be issued in due course, and that it would now hold further discussions with the three clubs regarding the implications of the decision.
Middlesbrough, who had called last week for Southampton to be kicked out over the scandal, issued a statement welcoming the decision, adding: "We believe this sends out a clear message for the future of our game regarding sporting integrity and conduct."
- With PA
