The 34 were issued two-year bans for doping in January, nearly three years after the Melbourne-based team announced an internal probe into a highly dubious supplements regime.
The scandal saw the Bombers, one of the Australian Football League's oldest and most storied clubs, stripped of 12 of their active players in the 2016 season and finish bottom of the 18-team table.
Although Essendon were sanctioned heavily by the AFL in 2013, disqualified from the playoffs and slapped with a record fine, the players fought to clear their names.
They alleged they were duped by staff and misled about the nature of the supplements they received during the 2012 season.
"All issues in these 18 cases have been agreed in-principle and subject to the paperwork now being satisfactory and being executed by our clients, the matters will be formally resolved in the next several days," lawyer Patrick Gordon, who represented some of the players, said in a statement.
The players' backdated ban ended earlier this month and most returned to pre-season training for the 2017 season.
(Reporting by Ian Ransom; Editing by Peter Rutherford)
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