It is not clear how many of the federal government's 2.3 million civilian employees will ultimately accept the offer, which promises to pay their salaries until October if they resign by Thursday.
Others are fighting the proposal in court.
Unions representing federal workers sued to block the "deferred resignation program" last week. A federal judge in Boston is to consider their request at 1 p.m. ET (1800 GMT) on Thursday.
Those who do not accept the offer have been told their jobs could be at risk as the administration moves ahead with its overhaul of government operations.
The buyout encompasses not only employees at domestic agencies like the Department of Labor that have traditionally drawn the ire of Trump's Republicans, but intelligence agencies like the CIA as well.