The Owls issued a statement announcing the appointment of administrators.
Despite the former Premier League club slipping further towards relegation as a result of the move, supporters expressed delight that the contested ownership of Thai businessman Dejphon Chansiri is over.
The EFL confirmed the points sanction but pointed out the process "presents Sheffield Wednesday with the opportunity to move matters towards a successful sale and secure future under new ownership."
Second-tier Wednesday said with creditors closing in, they had appointed an insolvency firm as administrators, following unsuccessful efforts to find a buyer.
Joint administrator Kris Wigfield said: "Like many football clubs, (Sheffield Wednesday) have been trading at a significant loss for several years, with those losses historically funded by the former owner Mr Chansiri.
"Due to increased financial pressure on the club, the owner has chosen to place the club and the stadium company into administration, which will enable us to market the club and the stadium as a whole, which is great news for supporters of the club."
The 12-point penalty leaves Wednesday on minus six points at the bottom of the Championship - 15 points from safety.
Fans have held protests calling on Chansiri to sell throughout the season, including during this week's 1-0 defeat against Middlesbrough at Hillsborough.
Thousands of supporters boycotted the game in a bid to force him out.
Wednesday failed to pay players and staff on time on five separate occasions this year, including in September.
Images on social media showed seats spelling out Chansiri's name in the North Stand at Hillsborough being ripped out, while there were also reports of fans queuing outside the stadium looking to buy tickets for Saturday's match against Oxford.
Even Culture Secretary Lisa Nandy had called on Chansiri to sell, and on Friday she said: "Having been in this position with my own team, Wigan Athletic, I know everyone who loves the club will be hoping for a resolution as soon as possible."
The Sheffield Wednesday Supporters' Trust described it as "one of the most bittersweet days in our club's proud 158-year history."
"Entering administration was the inevitable outcome of years of financial mismanagement, a lack of accountability and repeated failures to engage credible buyers," the Trust said in a statement.
"Administration is not to be celebrated. It needn't have ended this way. But we are overjoyed to have Dejphon Chansiri out of our club for good."
The Trust added that it "expects strong interest from prospective buyers" but that if a sale did not materialise, "supporters can be assured that, for the last few months, we have been working to develop a credible, fan-led takeover proposal".
"This ensures that even in the worst-case scenario, the threat of liquidation will not be an option."
