The penalty was brought in to encourage clubs to pay debts in full rather than use administration as a way of writing off money owed to creditors.
Now any club going into administration after the fourth Thursday in March will have the deduction suspended until it is known whether it will affect their league finish for that season.
If it makes the difference between survival and relegation it will be imposed that season, if not the club will start on -10 the following term.
The rule change was passed unanimously by chairmen at the League's AGM in Portugal.
"I am delighted that clubs have backed their board so strongly on this issue," said Football League chairman Lord Mawhinney .
"The changes we have made enable the League's 'Sporting Sanctions' regulations to remain true to their original aim.
"Clubs should suffer a sporting penalty as a consequence of going into administration, as this acts as a spur to better financial management."