Yi, a 40-year-old Ohio restaurant owner who also goes by the name Don, traveled to Seoul last month to attend his father's funeral.
But airport authorities prevented him from leaving the country on Feb. 6 because he faced a decades-old accusation of draft dodging.
South Korean police detained him for several hours. He was later released from custody but barred from leaving the country until March 2 pending review.
Prosecutors later said he was guilty, but they decided not to pursue the case, according to Yi.
Yi, who was born in Seoul but emigrated with his family at age 9, said he's not angry about the experience.
"I don't think anyone meant me harm, and I believe they have these laws in place for a reason," he told Stars and Stripes in a text message Monday from the gate while waiting for his flight.
He said all the officials he met were "sympathetic to my situation and were very professional."
Yi said he received American citizenship while serving in the U.S. Army from 2004 to 2012, including tours in Afghanistan and South Korea.
South Korea, which has faced a threat from heavily armed North Korea since their 1950-53 war ended in stalemate, requires all able-bodied men to serve some two years in the military.
It has strict rules governing conscription, including one that compels South Korean-born men to declare plans to remain abroad and change citizenship when they turn 18.
Yi failed to do so. He said he didn't realize he still had responsibilities in his native land and his detention resulted from a misunderstanding.
"I'm so excited to be going home," he said. "But once I embraced my situation I did get to enjoy many beautiful areas of Korea."
His advice to anybody who might find themselves in a similar situation is to check with the South Korean consulate in the United States before traveling to the peninsula.
Similar situations have occurred in the past due to South Korea's strict laws and attention to family bloodlines.
In one extreme case, an American man was forced into the South Korean military even though he was born in Champaign, Ill., to immigrant parents.
Young Chun, who wrote a book about his experience called "The Accidental Citizen-Soldier," went to teach English for a year in South Korea in 2002 only to learn his birthplace had been mistakenly entered in the official family registry system as Seoul.
The government said the then-22-year-old had to complete his mandatory military service or face prison.
In Yi's case, he received an outpouring of support from his community, fellow veterans and many servicemembers after he posted an appeal on Facebook.
Friends also started a GoFundMe page that as of Monday had raised $3,700 to help him.
"I have so much to be thankful for," Yi said.