The pleas were the first from Cullen, 44, who said last December that he had killed between 30 and 40 patients during the 16 years he worked as a nurse at 10 hospitals in Pennsylvania and New Jersey.
Cullen was charged with a murder and two attempted murders in Somerset County on Dec. 15 and initially said he intended to plead guilty.
But it took more than three months for him to do so, in large part because prosecutors from seven counties had to agree to the details of a guilty plea.
According to the deal, prosecutors will not seek the death penalty, and Cullen will cooperate with authorities in both states.
He faces consecutive life terms for the murders with no eligibility for parole for more than 120 years under terms of the agreement. A sentencing date was not set. Cullen will remain in custody pending sentencing.
Prosecutors were notified by Somerset Medical Center officials after the hospital fired Cullen on Oct. 31. An internal review had found questionable lab results involving six of Cullen's patients.
Somerset turned over information on the six cases to the prosecutor's office, said Dr. William Cors, the hospital's chief medical officer. All six patients had "multiple, serious medical problems," Cors said.
In August 1997, he was fired from Morristown Memorial Hospital for "poor performance," a spokeswoman for the hospital's parent company said.
Cullen worked at St. Luke's Hospital in Bethlehem, Pa., from June 2000 to June 2002, and resigned amid allegations that he had at least twice hidden unopened heart and blood pressure medications in a safety bin for used needles, Lehigh County District Attorney James Martin said.
St. Luke's spokeswoman Susan Schantz said the hospital was never subsequently contacted by anyone checking Cullen's employment references. "Had we been asked, we would have recommended that he not be hired," she said.
Cullen had no record of complaints or any disciplinary actions in New Jersey since he obtained a nursing license in the state in 1987, according to Genene Morris, a spokeswoman for the Division of Consumer Affairs.
Cullen also was licensed to work in Pennsylvania since June 1994, according to the Pennsylvania Department of State. His license was in good standing, officials said.
The families of some former patients who died while Cullen was employed at their hospitals are wondering whether their loved ones were among those the former nurse said he killed.
"My mom was in there and diagnosed with a high level of digoxin," Mary Ann Jones, whose mother died at Somerset Medical Center said. "I talked to my brother and sister, and they want this investigated."