The couple and their lawyers are scheduled to return Monday to the Union County Courthouse to begin settlement talks on remaining issues, including alimony and child support.
Should those succeed, the final issue would be Dina Matos McGreevey's claim of marriage fraud.
James McGreevey left the courthouse Thursday evening escorted by two uniformed sheriff's officers. Speaking of the custody agreement for his daughter, McGreevey said, "She'll get a large amount of time to spend with her parents."
Moments later, lawyers for both McGreevey and his wife stood together before television cameras and reporters, saying they could not disclose terms of the custody agreement because it was confidential.
"It was an amicable settlement," said John N. Post, lawyer for Matos McGreevey. "The judge was very, very helpful to both sides."
Asked about the financial and fraud issues that remain, Post said, "Hopefully we'll be able to settle those issues also."
Stephen P. Haller, lawyer for the former governor, said his client is "delighted" with the custody agreement. "But the issues that remain are markedly different with different consequences," he said.
He said the McGreeveys spoke to each other during the discussions, and, "If I were their daughter, I would be proud of how my parents were able to work together."
Thursday's testimony was given behind closed doors because it dealt with custody of the child. There was no immediate word on who or how many people had testified.
The former governor and his wife split in 2004 after he resigned in disgrace over a gay affair. They had been married for four years.
James McGreevey stepped down during his first term in office after a nationally televised speech in which he acknowledged being "a gay American" and said he had an affair with a male staffer. The staffer has denied the affair and claims he was sexually harassed by McGreevey.
In the 3½ years since the breakup, James McGreevey took up residence at the home of his boyfriend and began studying for the Episcopal priesthood while Matos McGreevey became a sometime analyst on cable television shows. Both wrote tell-all books and promoted them on Oprah Winfrey's television show.
Matos McGreevey claims she was duped into marriage by a closeted gay man who needed the cover of a wife to advance his political career. James McGreevey contends she should have known he was gay and that the marriage was "a contrivance on both our parts."
