They had arrived in Muscat late on Wednesday night from Tehran under a US$1mn bail-for-freedom deal.
Addressing the media at Muscat International Airport's VIP lounge shortly before their departure, both Fattal and Bauer expressed their gratitude to His Majesty the Sultan in their farewell message.
Both appeared calm and composed as they read out from a prepared statement.
"We will always be grateful to His Majesty Sultan Qaboos bin Said of Oman for his efforts to secure our release," said Bauer.
"Getting off the plane right here three days ago was the most incredible experience of our lives. We will never forget the excitement of seeing our loved ones waiting for us at the foot of the plane. The joy of embracing them all after so long will stay with us forever," he added.
Following the reunion with their families and relatives after over two years in prison, where they were held on charges of spying, the two Americans were given complete privacy and kept away from the public.
However, an official source told Muscat Daily that the released hikers along with their families visited the Sultan Qaboos Grand Mosque as well as the Muttrah souq.
"Just hours after we left prison, we were able to swim in the calm waters of the Gulf.
"We stayed up all night with our loved ones and watched the most beautiful sunset we have ever seen. These experiences will be with us for the rest of our lives. We would like to thank Oman for welcoming us and hosting our families," said Fattal.
The two, along with another American Sarah Shourd, were detained in July 2009 along the Iran-Iraq border. In an identical scenario, Shourd who is also Bauer's fiance, was released last September on a US$500,000 bail with Omani mediation. She had spent a few days in Muscat as well before flying home.
The released American hikers also acknowledged the efforts of Dr Salim bin Nasser al Ismaily, CEO, Omani Centre for Investment Promotion and Export Development, in securing their release.
"We thank His Majesty's envoy Dr Salim al Ismaily from the bottom of our hearts for his selfless efforts to make our freedom a reality," Bauer said.
Dr Ismaily was instrumental in the three-way negotiations between Oman, Iran and the US for the release of the hikers on both occasions.
However, the official source revealed that ‘the release this time was tougher and took marathon sessions of negotiations to finally reach an amicable settlement’.
While thanking the US Ambassador to Oman, H E Richard J Schmierer and his wife Sandy, Fattal said, "We hope some day to return to this wonderful country. But for now we are eager to get home at last."