At a meeting on Wednesday the EFL board “unanimously” decided on a plan, but now clubs need to support it.
On 21 May, the new structure was set out including the remaining promotion, relegation, and play-offs.
League Two teams have already confirmed that they intend to finish the season, but League One sides remain undecided.
Championship clubs whose players returned to Monday’s training expect to restart their campaign in June.
To date, two rounds of coronavirus testing have been carried out in the 24 second-tier clubs, with more than 1,000 tests conducted each time.
Two people at Hull City tested positively in the first round revealed on Sunday, and in the second round of testing two unnamed Fulham players and Blackburn captain Elliott Bennett tested positive.
On Thursday, the Premier League announced a tentative restart date of 17 June with up to six games at neutral venues. The EFL said they planned to play on the home grounds of clubs for all remaining fixtures.
Clubs were given to continue sending any alternate ideas for how the system would operate until next Tuesday.
A 51 percent majority of Championship, League One, and League Two clubs are expected to authorize the campaign curtailment in each division.
Unweighted points-per-game will determine final league placings in all three divisions unless the respective seasons can be completed.
The National League, meanwhile, must await an EFL decision on how to conclude the League Two campaign before deciding on their next moves.
The regular season is over at non-league level, but the National League aims to retain two teams being promoted to the EFL, which could include scheduling play-off games.