The "Ghost Dance" shirt was taken to Scotland in 1891 by Buffalo Bill Cody's Wild West show, and has been at Kelvingrove Art Gallery in the city ever since. Stained with blood, it is a relic of the Ghost Dance religion that sprang up in the 1880s among native Americans, who believed it would give them immunity to enemy bullets.
Last year councillors decided to return it, in response to a request of the association representing survivors from the Battle of Wounded Knee, said to be a massacre in which more than 200 Sioux were killed by the US Seventh Cavalry in 1890.
The Glasgow delegation of three will fly to South Dakota on 31 July for ceremonies at the site of Wounded Knee in the Pine Ridge Reservation, and at the museum of the South Dakota Historical Society in Pierre where the shirt will be showed.
Native Americans were unaware the shirt still existed until 1992, when an American lawyer, John Earl, saw it in Glasgow and started a campaign to bring it home.