"She'll get a large amount of time to spend with her parents," McGreevey said of his daughter as he left the courthouse escorted by two uniformed sheriff's officers.
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, who represents Dina Matos McGreevey.
Stephen P. Haller, the former governor's lawyer, said his client was "delighted" with the custody agreement. "But the issues that remain are markedly different with different consequences," he said.
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 remaining issue would be Dina Matos McGreevey's claim of marriage fraud.
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.
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 31/2 years since the breakup, 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.