Mr Weeks (50) and Mr King (63), who were grabbed outside the American University in Kabul in 2016, were freed in exchange for three members of the Taliban's Haqqani Network.
The two men were handed over to US forces in Afghanistan's southern Zabul province and flown out in a US helicopter, The Associated Press reports.
White House press secretary Stephanie Grisham indicated Mr Weeks, from Wagga Wagga in NSW, was in the care of US officials and receiving medical care.
Mr Weeks' father Mervyn was notified of his release in a phone call from the Department of Foreign Affairs and Trade.
Mervyn Weeks told the ABC he was very relieved but that he had yet to speak to his son and was unsure of his whereabouts and plans.
A Weeks' family statement on Tuesday night asking for privacy.
"We are grateful for the efforts of the Australian government in securing Tim's release," it read.
"We would like to thank the United States government for the significant role it played in securing Tim's freedom and acknowledge the important contribution of the government of Afghanistan.
"We thank our friends and extended family for their love and support over the past three years during this very difficult time.
"While we understand the intense public interest in Tim's release, we do not want to comment further."
Australian Prime Minister Scott Morrison late on Tuesday night tweeted his relief at Mr Weeks' release and said he was "profoundly pleased".
Mr Morrison issued a joint statement with Foreign Affairs Minister Marise Payne which thanked US President Donald Trump and Afghan President Ashraf Ghani.
"We regard this release as one of a series of confidence-building measures that are taking place in Afghanistan. We hope that such measures will set the stage for a ceasefire and intra-Afghan dialogue," the statement read.
Mr King's family released a statement saying he was also safe with US officials and getting the medical care he needs before his return home to be reunited with his family.
