The cost of coronavirus testing and extending player contracts were major factors in the decision.
The Premier League and second-tier Championship have invested in a testing programme, with both leagues set to resume next week.
Promotion and relegation have been retained in League One and League Two, while playoffs to determine a final promotion place in each division will still take place.
In League One, Coventry and Rotherham are promoted to the Championship, while Oxford, Portsmouth, Fleetwood and Wycombe will contest the playoffs.
Bolton, Southend and Tranmere are relegated to League Two.
Crewe, Swindon and Plymouth take their places in League One.
At the bottom of the table, Stevenage could be saved from relegation by a further points deduction for Macclesfield for failing to pay players on time.
Exeter, Colchester, Cheltenham and Northampton will contest the League Two playoffs, starting on June 18.
The League Two playoff final will take place at Wembley on June 29.
“Whilst it has always remained the board’s position to play the remainder of the season where possible, the decision reached at today’s meeting follows a full and considered consultation period with our member clubs,” said EFL chairman Rick Parry.
“The board has endeavoured to listen to all views and alternative approaches but understands that the decisions taken will not be met with universal satisfaction from all clubs.”
The Championship is due to return on June 20 with the remaining nine rounds of fixtures crammed in to just over a month.
However, should a spike in infections cause the season to be curtailed once more, points-per-game would also determine the standings of the second tier.
Leeds are on the verge of ending a 16-year wait to return to the top-flight. Marcelo Bielsa’s men lead West Bromwich Albion by a point at the top of the table and hold a seven-point advantage over third-placed Fulham.
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