A U.S. couple cleared in the death of their 8-year-old daughter arrived home to Los Angeles on Thursday and reunited with family members following a legal battle that kept them in Qatar for nearly two years, including almost a year spent in jail.

Matthew and Grace Huang arrived with smiles on their faces, according to The David House Agency, which represents them.

"Mission accomplished. Matt and Grace are in Los Angeles. They have not stopped smiling," the agency tweeted.

The agency later tweeted a photo of the couple embracing their sons and other relatives, saying it was a "Glorious family reunion. If the Qatari prosecutors could only see this moment!"

The Huangs gained international attention when they were arrested in January 2013 on charges of starving their African-born daughter, Gloria, to death.

The couple, who are of Asian descent, had adopted Gloria in Ghana when she was 4 years old, and are the parents of two other adopted, African-born children.

Throughout the case, the family's representatives expressed concern that there were cultural misunderstandings underpinning the charges against the couple in a nation where Western-style adoptions and cross-cultural families are relatively rare.

An initial police report raised questions about why the couple would adopt children who did not share their "hereditary traits."

Prosecutors said the couple denied food to their daughter and locked her in her room at night. The Huangs said Gloria suffered from medical problems complicated by an eating disorder that was the result of her impoverished early years in Africa.

The Huangs spent nearly a year behind bars before their case was heard for the first time in November 2013. They were eventually convicted of child endangerment and sentenced to three years in prison.

An appeals court judge overturned their conviction Sunday and said they could leave, but their passports were confiscated at the airport later that day.

Their situation remained tense until the moment of their departure Wednesday, with Matthew Huang being detained for several minutes at the airport's passport control station as his wife watched in tears.

The suspense encapsulates the twists and turns of a slow-moving case that became an irritant in otherwise close relations between the U.S. and Qatar, a key ally that hosts an important U.S. military air base.

"We feel relieved. We feel gratitude to the legal system in the state of Qatar, which after some time worked as a good legal system should," said U.S. Ambassador to Qatar Dana Shell Smith, who accompanied the couple to the airport.

The couple and their children moved to Qatar in 2012 after Matthew Huang was hired to work as an engineer as part of preparations for the 2022 World Cup.