A pair of American hikers who spent two years in prison in Iran returned to the United States on Sunday.

Josh Fattal and Shane Bauer landed at New York’s John F. Kennedy International Airport shortly before 11 a.m. They had been held in Iran as accused spies since July 2009, after they apparently strayed over an unmarked border between Iraqi Kurdistan and Iran.

The crew of their U.S.-bound flight moved them to the front of the aircraft before landing, allowing them to get off the plane first. Fattal had a big grin on his face as he moved forward.

Iranian authorities released Fattal and Bauer on Wednesday. They first were flown to Oman, where they enjoyed several days of freedom after their lengthy captivity.

The two are expected to hold a news conference Sunday afternoon. In their prepared remarks, Fattal and Bauer are expected to be frank about their experience and conditions in Iran.

Fattal and Bauer, both 29, say they accidentally crossed into Iran when they veered off a dirt road while hiking near a tourist site in the Kurdish region of northern Iraq. They appealed their eight-year sentences while serving time in prison.

A third American seized with them, Sarah Shourd, was freed on medical grounds almost exactly a year ago. Shourd and Bauer became officially engaged Friday.

In statements before leaving Oman’s capital Muscat, Bauer and Fattal thanked Omani officials for their hospitality and assistance in securing their release.

“Just hours after we left prison, we were able to swim in the calm waters of the Gulf,” Fattal said. “We stayed up all night with our loved ones and watched the most beautiful sunrise we have ever seen. These experiences will be with us for the rest of our lives.”

Fattal and Bauer were released a day before Iranian President Mahmoud Ahmadinejad’s address to the United Nations. Shourd’s release came a week before Ahmadinejad addressed the United Nations last year.

CNN’s Susan Candiotti, Todd Baxter and Mohammed Jamjoom contributed to this report.