Trevor Reed had been held in a Russian jail since 2019. He was traded for Konstantin Yaroshenko, a Russian jailed on drug-smuggling charges.
Speaking outside the Reed home in Texas, his mother said she felt “almost as good as the day he was born”.
Reed is currently on his way back to the US, where he is expected to spend several days in hospital.
President Joe Biden said he had been “delighted” to share the news of Mr Reed’s return with his parents in a phone call.
“The negotiations that allowed us to bring Trevor home required difficult decisions that I do not take lightly,” he said.
According to parents Joey and Paula Reed, their son was poorly treated in prison and appeared to have contracted tuberculosis.
The couple protested outside the White House last month, ultimately securing a meeting with the president.
In a media interview outside their home in a suburb of Dallas on Wednesday, they thanked Mr Biden, who his father said “probably saved our son’s life”.
They added that Mr Biden’s phone call came while they were on the other line with their son. When they told the president they were at that very moment speaking with Trevor, Mr Biden told them to hang up on him.
“Anyone who says he’s [Mr Biden’s] not a compassionate or kind man is just a liar or an idiot,” his father said about Mr Biden.
Mr Reed, 30, went to Moscow in 2019 to learn Russian and visit his Russian girlfriend.
