Shane Bauer and Josh Fattal, both 29, ran across the tarmac into the arms of their tearful parents and siblings after the Omani air force aircraft touched down in the capital early yesterday.
The two, who spent 782 days in jail for espionage in Iran, were released late on Wednesday as part of a US$1 million (Dh3.67m) bail deal brokered by Oman.
"They are exhausted. They need rest and a medical check-up before travelling to US on Friday," an Omani foreign ministry official said.
Sarah Shourd, Mr Bauer's fiancee, was also there to greet them. Ms Shourd was arrested with Mr Bauer and Mr Fattal but she was released last year in a similar deal mediated by Oman. Mr Bauer proposed marriage to Ms Shourd while they were in prison.
The three have denied they were US spies.
"Two years is too long to be in prison. We sincerely hope for the freedom of other political prisoners and other unjustly imprisoned people in America and Iran," Mr Bauer told reporters after landing in Muscat.
Mr Fattal added: "We're so happy we are free."
The US president, Barack Obama, said the release was "wonderful, wonderful news about the hikers, we are thrilled".
Mr Bauer and Mr Fattal both travelled from the prison to the Tehran airport, where the Omani plane was standing by to fly them out.
Present at their release were the Swiss ambassador - the Swiss embassy handles US affairs in Iran - and an Omani delegation.
Mr Fattal and Mr Bauer had been sentenced to eight years in prison on charges of espionage and illegal entry on July 31.