The deal also guarantees space for three charter schools given the boot by New York City Mayor Bill de Blasio and gives charter schools $40 million to pay rent if they can't get space in a public school.
Also, per pupil funding for charter schools will jump by $1,100 over three years.
Charter schools currently get about one third less than traditional public schools.
Legislators are expected at the Capitol in Albany for a rare Friday appearance in an effort to close remaining differences among themselves and the governor's office on plans to spend more than $140 billion in the coming fiscal year.
Cuomo and legislative leaders have been meeting through the week while subcommittees of state senators and Assembly members and staffs have tried to work out a final budget and accompanying legislation for the new year that starts Tuesday.
They hoped to resolve final differences and print legislation Friday, clearing the way for Monday voting since bills usually need to sit on lawmakers' desks for three days.
Issues include funding levels for public schools, including pre-kindergarten, as well as property, inheritance and business tax breaks.
(The Associated Press contributed to this report)
