Smith and Yates, of Morehead, Kentucky, have been together for nearly a decade. They arrived at 8:05 a.m., five minutes after the office opened, and became the first same-sex couple to get their marriage license in Rowan County's history.
After the men paid the $35.50 fee, deputy clerk Brian Mason said, "Congratulations." They said this was their sixth attempt to get a license.
Yates rushed to embrace his mother in a long hug.
When Yates and Smith exited the courthouse, they were met with cheers from about 35 supporters, chanting, "Love wins."
Davis was jailed Thursday after a judge found her in contempt of court for her refusal to issue marriage licenses to same-sex couples. But five of her deputies said under oath they would comply with the court's order to issue the licenses.
Davis' stay in jail has not made her reconsider her stance on issuing the licenses, her attorney Matthew Staver told ABC News.
"One thing about Kim, she may be incarcerated behind the jail bars but her conscience remains free," Staver said. "And just knowing Kim, she's made a decision and she can't violate that conscience and she can't have this collision with her religious convictions."
Yates said, "I just want the licenses given out. I don't want her in jail. No one wanted her in jail."
Yates and Smith plan to wed in a small ceremony at Yates' parents' home.
The second same-sex couple to be granted a marriage license in Rowan County today was Tim and Michael Long, who arrived at 9:30 a.m. They said they had been denied a license one week ago.
They said they have been a couple for 9 years and celebrated their relationship in a civil commitment ceremony in 2008, when Michael took Tim's last name.
After emerging from the clerk's office with their license today, the Longs raised their joined hands up high and kissed.
Both are longtime residents of Rowan County. They said they didn't want to get a marriage license in another county because this is their home, this is where their friends are and this is where they pay their taxes.
"I still feel the hate, but it doesn't feel as bad because today love won," Tim Long said.
They said they plan to have a wedding on Sept. 27.
The Associated Press contributed to this report.