I did my thesis on this! The short of the story is that after the purchase Russian America (Alaska) by William Seward in 1867, ther became an increase in settlers who were hunting with firearms that the native Alaskan population did not use. The prevailing thought at the time was that they were being both overhunted and scared back into the Yukon by the firearms.
Reverend Sheldon Jackson, the General Agent of Education in Alaska who first came with his wife as a missionary, went on a cruise on the Revenue Cutter BEAR (Revenue Cutter Service ship/now the Coast Guard) with Captain Michael Healy. Healy and Jackson both saw the effect that commercial hunting and fishing were having on the natives, as caribou were becoming hard to find and were so crucial to the way of life, as well as the sea otter becoming increasingly rare. Healy had been to Siberia where reindeer were successfully herded. In September of 1891, Jackson, Healy, and 16 reindeer came from Siberia to Alaska, where the reindeer not only survived the winter, but also created a little reindeer calf. In the summer of 1892, Healy delivered 171 reindeer and 5 native Siberian herders to teach the native Alaskans how to herd.
Charlie Antisarlook would become the posterchild of the herder movement, and even after his death, his wife, known as Sinrock Mary, would become the queen of the herder movement.
Today, only native Alaskans can own and herd reindeer. Also, reindeer do not like to have their antlers petted even though they are incredibly soft (they're super sensitive). Yes, I learned this the hardest way possible. Reindeer can hurt you.
Funfact: Jackson had very racist views against the natives and wanted to make them herders instead of hunters, and Healy helped make this possible. Healy is a powerful figure, even in today's Coast Guard, as he was half Black and joined during the civil war, but hid it from even his family. He was also an Irish Catholic, and tried to kill himself twice. Because of his second attempt, he was sent to land and missed out on captaining the greatest ever rescue in the Coast Guard: The Overland Expedition. But that's a whole 'nother story.