ALBANY — Gov. Andrew M. Cuomo and legislative leaders on Sunday night reached an agreement on the next state budget, capping weeks of deliberations over issues like deterring public corruption and improving public schools.

The pact includes education reforms as well as several new ethics measures that Mr. Cuomo proposed in response to the seemingly never-ending series of scandals in Albany. The marathon of malfeasance was punctuated in January by the arrest of Assemblyman Sheldon Silver, who at the time was the Assembly speaker, on federal corruption charges.

The budget, which still needs the formal approval of lawmakers, would be the state’s fifth in a row passed by the April 1 deadline. All of those spending plans were crafted by Mr. Cuomo, who has proudly boasted of his perennial punctuality in a capital where budgets had been chronically late.

“With this agreement, we address intractable problems that have vexed our state for generations,” Mr. Cuomo said in a statement.