07/03/2013 AT 03:30 PM EDT
Add John Barrowman to the list of people who have raced to the altar following the Supreme Court's decision last week to legalize gay marriage
in the state of California.
actor, 46, married Scott Gill on Tuesday. The couple, who have been together for 20 years, had been in a civil partnership since 2006.
"We're on our way to get married," a jolly Barrowman said in a video
he posted Tuesday on his WhoSay account, with Gill in the passenger seat.
The happy couple then began belting out the lyrics to Air Supply's "All Out of Love," which conveniently happened to come on the radio, mid-video.
"About time we get married," Barrowman, who also starred on Doctor Who
, went on to say. "Thank you, everybody!"
The pair couldn't contain their excitement and went ahead with an additional video, in which Barrowman, who was still driving, told the camera, "We're getting married in the state of California. Thank you, Supreme Court. About time you made it legal! Yay!"
Following a quick smooch, the actor looks at the camera and says, "See you after we have the [ceremony]."