"I have been so touched and moved, beyond all words, by the people who have come up to me today — strangers on the airplane, the flight attendants, and most of all my family — to say welcome home," Curtis said in the statement.
He also said he was "deeply indebted" to the U.S. officials who worked to get him released.
Curtis, 45, of Boston, was released by al-Nusra Front, a Sunni extremist group.
Last week, journalist James Foley, who also was kidnapped in 2012 while covering the Syrian uprising, was killed. The Islamic State group posted a Web video showing his beheading.
The extremists said they killed the Rochester, New Hampshire, resident in retaliation for U.S. airstrikes targeting Islamic State positions in northern Iraq.
Curtis' mother said she was "overwhelmed with relief" that her son had been returned to her. "But this is a sober occasion because of the events of the past week," she said. "My heart goes out to the other families who are suffering."
U.S. freelance journalist, Austin Tice of Houston, disappeared in Syria in August 2012. He is believed to be held by the Syrian government.