(CNN) — A nurses strike at two private New York City hospital systems has come to an end after 7,000 nurses spent three days on the picket line.

The New York State Nurses Association union reached tentative deals with Mount Sinai Health System and Montefiore Health System, which operates three hospitals in the Bronx that had been struck. The nurses had been arguing that immense staffing shortages have caused widespread burnout, hindering their ability to properly care for their patients.

The union said the deal will provide enforceable "safe staffing ratios" for all inpatient units at Mount Sinai and Montefiore, "so that there will always be enough nurses at the bedside to provide safe patient care, not just on paper." At Montefiore, the hospital agreed to financial penalties for failing to comply with agreed-upon staffing levels in all units.

Montefiore said the agreement also includes 170 new nursing positions, a 19.1 percent increase in pay, lifetime health coverage for eligible retirees, and adding "significantly more nurses" in the ER.

The deals were announced in the early hours Thursday morning — at 3 a.m. ET for Montefiore and about 30 minutes later at Mount Sinai. The nurses were expected to be back on the job for the 7 a.m. ET shift Thursday, and Montefiore Medical Center said all surgeries and procedures and outpatient appointments for Thursday and after will proceed as scheduled.

Nurses will need to vote to approve the deal before it is finalized. But the union said the tentative deal will help put more nurses to work and allow patients to receive better care.

"Through our unity and by putting it all on the line, we won enforceable safe staffing ratios at both Montefiore and Mount Sinai where nurses went on strike for patient care," the nurses union said in a statement. "Today, we can return to work with our heads held high, knowing that our victory means safer care for our patients and more sustainable jobs for our profession."

Mount Sinai called the agreement "fair and responsible."

"Our proposed agreement is similar to those between NYSNA and eight other New York City hospitals," Mount Sinai said in a statement. "It is fair and responsible, and it puts patients first."

"From the outset, we came to the table committed to bargaining in good faith and addressing the issues that were priorities for our nursing staff," Montefiore said in a statement. "We know this strike impacted everyone — not just our nurses — and we were committed to coming to a resolution as soon as possible to minimize disruption to patient care."

The hospitals had stayed open during the three-day strike, using higher-cost temporary nursing services to provide care, and transferring other employees to take care of non-medical nursing duties. They had also diverted and transferred some patients to other hospitals and postponed some elective procedures.

The striking nurses have said they are working long hours in unsafe conditions without enough pay — a refrain echoed by several other nurses strikes across the country over the past year. They said the hours and the stress of having too many patients to care for is driving away nurses and creating a worsening crisis in staffing and patient care.

The union representing the nurses had reached tentative agreements offering the same 19 percent pay hikes at other New York hospitals, avoiding strikes by about 9,000 other nurses spread across seven hospitals in the city. But the nurses at the hospitals that went on strike said the pay raises weren't the main problem, that the more severe staffing shortages at Mount Sinai and Montefiore needed to be addressed before a deal could be reached.

Both hospitals had criticized the union for going on strike rather than accepting offers they described as similar to those the union accepted at other hospitals in the city.

-- CNN's Chris Isidore contributed to this report

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