The Legislature and Cuomo agreed to make NY the second state in the nation to ban single-use plastic bags.
There are still a few moving parts to the budget, but Senate Leader Andrea Stewart-Cousins said some of the remaining items -criminal justice reform, public financing of campaigns and increasing school aid funding - are "within striking distance of being resolved".
NY lawmakers are expected to begin passing the budget on Sunday.
The ban would prohibit grocery stores from providing plastic bags for most purchases - something California has been doing since 2016.
New York State is set to become the second state in the United States to ban plastic bags and soon you could be charged for using paper bags.
Gov. Andrew Cuomo has been attempting to pass the measure since he first brought it up during last year's budget battle.
With a Sunday night deadline looming, the NY state budget is starting to take shape.
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It also places a fee on handing out paper bags. New York's environmental advocates have also echoed this concern.
"Every mandated cost increase adds up", said Greg Biryla, New York director of National Federation of Independent Business.
But in an interview with NBC News' Madani, Todd Kaminsky, a Democratic state senator from Nassau County and chairman of the Environmental Conservation Committee, said he believes New York's plastic bag ban was long overdue. "I also said this budget must be done right - meaning it must be fiscally responsible and protect NY from the federal government's ongoing economic assault on our state". State lawmakers are working to finalize the proposal ahead of Monday's deadline, officials told the AP Friday.
NY is set to become the second state in the country to ban plastic shopping bags, but it will be up to its counties and cities whether to charge a fee for paper.
"New York had a chance to show real leadership and came up short", said Peter Iwanowicz, executive director of Environmental Advocates of NY, according to the Times.
One of the other big issues of the year - the legalization of recreational marijuana - will not be included in the budget.