The actor announced the news on photo and video-sharing site WhoSay and thanked the Supreme Court for making marriage legal in California.
In the video, the 'Torchwood' star says: "It's five after one and we've got our coffee and we're in the car getting ready to leave, because where are we going, Scott?"
The star then turns the camera to his partner, who replies: "To get married. Yay!"
The 'Torchwood' star then adds: "We're getting married in the state of California. Thank you Supreme Court, about time you made it legal. See you after we have the ceremony!"
The newly- married couple - who had previously entered into a civil partnership in the UK - later posted a snap of themselves holding their marriage certificate, writing: "We are now legally married. Thanks for all your great wishes. JB and Scott."
Last week the Supreme Court overturned the controversial Defence of Marriage Act, which banned same-sex marriage.
Congrats to them both!