The four planned to drive to the Egyptian border and fly out of Egypt, said Buddy Shadid, the father of Times reporter Anthony Shadid.
"They were wanting to keep it quiet yesterday because of the delicate negotiations," Buddy Shadid told The Associated Press.
"Apparently the United Nations and Turkey and some other nations all put pressure on the Libyan government to release them."
Buddy Shadid said he had spoken to his daughter-in-law, Nada Bakri, who said the four journalists were treated well and had plenty of food and water.
The journalists are reporter Anthony Shadid; photographers Tyler Hicks and Lynsey Addario; and a reporter and videographer, Stephen Farrell. In 2009, Farrell was captured by the Taliban in Afghanistan and was rescued by British commandos.
Gadhafi's son, Seif al-Islam Gadhafi, told ABC News reporter Christiane Amanpour during an interview that the journalists were in Libyan custody, and on Thursday evening Libyan government officials told the U.S. State Department that all four would be released, the Times said in an article on its website. A Times spokeswoman declined to comment.
The journalists had last been in contact with editors on Tuesday from the northern port city of Ajdabiya where they were covering the retreat of rebels.
Hicks' father, Portis Hicks, said his son called him briefly Thursday while still in Libyan custody. Tyler Hicks said he was in good health was being treated well.
"We are relieved and very gratified that the Libyan government has agreed to release them," Hicks said.
Buddy Shadid said the ordeal had left family members emotionally drained.
"I didn't know if he was in a car that got blown up or something like that, and they couldn't identify the bodies. My imagination ran wild," he said.
Shadid had worked previously for The Associated Press, Washington Post and Boston Globe. He won the Pulitzer Prize for international reporting in 2004 and 2010 for his coverage of Iraq.
Hicks, a former photographer for The Wilmington Star-News in North Carolina and the Troy Daily News in Ohio, was named Newspaper Photographer of the Year in 2007 by Pictures of the Year International and won an Infinity award from the International Center of Photography in 2001.
Portis Hicks said his son had once been detained for a few days by the Russian army during an assignment in Chechnya.
Addario also has worked for National Geographic and Time magazine and was part of The New York Times team that won the 2009 Pulitzer Prize for international reporting. She won a MacArthur Fellowship, known as the Genius Grant, in 2009.