Wild, a 28-year-old born in Washington state, previously competed for the United States but got frustrated with the lack of funding for downhill snowboarding.
He married Russian snowboarder Alena Zavarzina - who won Bronze in the women's event just minutes before Wild won Gold - and became a Russian citizen in 2012.
"I want to thank Russia for giving me the opportunity to win a gold medal", he said after the win, which gave Russia its first Gold in a snowboard event at the Olympic Winter Games. "My teammates helped me so much. I don't think many of them like me, but I really appreciate it".
The fiercely partisan, flag-waving crowd that was packed into the stands at Rosa Khutor Extreme Park were loud and boisterous in their support for Wild, who admitted to reporters after his race that while he liked living in Moscow, he was not really able to speak Russian.
Galmarini, who beat Wild in the first of the two final runs but could not repeat it in the second, said he had quit his job a year ago to train full time. "I had a lot of fifth or sixth places but never got on the podium. I had to get angry enough about that to get on the podium today".
Zan Kosir (SLO) won the bronze medal after beating Patrick Bussler (GER) by a comfortable margin in the race for third.