"The boys and I worked so hard for this and we don't want to stop here, just at the Europeans, we want to keep focusing on trying to do our best when we get out to Beijing," said Mouat, the 27-year-old men’s team skip after success in Lillehammer, Norway, where they won every match.
Mouat, a member of the the Gogar Park club based at Murrayfield in the Capital, was supported by Grant Hardie, Bobby Lammie, Hammy McMillan, alternate Ross Whyte and coach Alan Hannah.
He said: “I’m just really proud of everyone who’s put in all the work. I’m going to enjoy this one.”
Victory lays down a marker for Beijing after previous disappointments against the Swedes.
Swedish skip Niklas Edin got the better of Mouat in the World Championship final in April and the Swedes have dominated recent European Championships, winning five of the past six titles.
Muirhead was joined by long-serving team-mates Vicky Wright and Jen Dodds, along with newcomers Hailey Duff and Mili Smith.
She said: "A wee while back that I never thought that I would be top of the podium after my hip surgery and having been through a tough few months, but here we are.
"To do it alongside Hailey and Mili when they are making their debuts at this level, and Vicky and Jen who were winning their first gold medals, is something really special and I'm very very proud of them."
Muirhead, Dodds and Wright had suffered disappointment at the World Championships in May, failing to secure an Olympic place when they finished outside the top six. However, they have one more chance to reach Beijing 2022, with a final qualifying tournament offering three further places.