By Erica Orden and Mike Vilensky 

ALBANY--Gov. Andrew Cuomo and legislative leaders struck a deal late Sunday evening for a state budget that will implement new income-disclosure policies for lawmakers and changes to the teacher-evaluation process and teacher-tenure policies.

The centerpiece of the budget agreement, an ethics overhaul, will require state lawmakers to disclose sources of outside income exceeding $1,000 a year, as well as the services they perform to receive it. And it will force those who work as lawyers to disclose the identity of their clients, with exceptions to be approved by the state ethics agency or the Office of Court Administration.

Under the agreement, lawmakers will be saddled with a burden of proof in exchange for their per diems. The plan calls for legislators to use an electronic swipe-card system to demonstrate their attendance in Albany before they receive compensation for their travels.

The ethics package is the third ethics overhaul in the four years since Mr. Cuomo took office.

The governor's push to overhaul public education, partly through instituting a new teacher-evaluation system, was one of the most contentious holdups. The budget agreement puts the job of refining the teacher-evaluation process in the hands of the state education department, and ties evaluations to teacher tenure, which will be available after four years, instead of the current three.

A joint statement released Sunday by the governor's office and legislative leaders noted that the deal boosted school aid by $1.4 billion, to $23.5 billion, without specifying changes that the governor said in his budget request he would require as a condition of increasing school funding.

United Federation of Teachers president Michael Mulgrew praised the deal because it didn't raise the cap on charter schools, add individual merit pay or alter due process rights for teachers.

But the spending plan contains few other major policy initiatives--a consequence of the governor's insistence on including the package of ethics overhauls.

Mr. Cuomo, a Democrat, appeared to sacrifice leverage on other agenda items when he prioritized ethics overhauls, saying he wouldn't sign off on a budget deal that excluded that package.

The bulk of it did end up in the budget.

But cut out of the spending plan were many of the other items Mr. Cuomo highlighted in his combined state of the state and executive budget address earlier this year, including raising the cap on charter schools; mayoral control of schools, an issue New York City Mayor Bill de Blasio has advocated; a measure that would bar minors from being tried as adults; and a plan for an independent monitor for police brutality cases.

Also excluded were a proposal that would open state tuition assistance to illegal immigrants, an education tax credit and an increase in the minimum wage.

Mr. Cuomo said on Saturday that he put forth an ambitious list of budget initiatives to lay out his priorities, but that many of the measures can be dealt with after the budget is passed.

Because of the timing of the deal, Cuomo administration officials said, the governor will issue an executive "message of necessity" to waive the required three-day aging period that New York budget bills must have before a vote.

The budget deadline is Wednesday, meaning lawmakers must vote on the spending plan by Tuesday in order for the budget to be completed on time. Because the deal was struck late Sunday night, legislators will have limited time to read the voluminous budget bills before voting.

Assembly Speaker Carl Heastie said struggling schools would be given extra resources for social services to help at-risk students, and the New York City schools chancellor would be given time to implement her plans to turn around the most troubled schools. How to extend mayoral control, which expires in June, will be discussed after the budget, he said.

The deal struck over the weekend sets Mr. Cuomo up for his fifth consecutive on-time budget, an achievement he has touted in the past to illustrate his ability to bring functionality to the historically obstinate state legislature.

The budget process this year was upended by several incidents, most notably the replacement of Sheldon Silver, the longtime Democratic assembly speaker who was forced out of his leadership post after his arrest on federal corruption charges, with Mr. Heastie.

Mr. Silver, who remains an assemblyman representing Manhattan, has said he is innocent.

It was also then rattled by objections from minority leaders to their exclusion from the private meetings the governor and legislative leaders traditionally hold to negotiate the budget.

After minority leaders, particularly Sen. Andrea Stewart-Cousins, began to demand entry to the meetings, Mr. Cuomo stopped holding them, instead conferring by phone or individually with Mr. Heastie or Senate Majority Leader Dean Skelos.

Legislative leaders, however, voiced few complaints with the process or its outcome. Speaking to reporters outside his office on Sunday evening, Mr. Heastie noted that "there are a couple of disappointments--we'd like to see the minimum wage [increase]," he said. "But outside of that, I think this is a pretty good budget."

Write to Erica Orden at erica.orden@wsj.com and Mike Vilensky at mike.vilensky@dowjones.com