"We feel very fortunate to have started the New Year this way," the couple tells PEOPLE. "With an abundance of love and happiness together, shared with all of our friends and family."
Satine, 26, who plays Judi Silver on the Starz series Magic City, wore a gown designed by Inbal Dror for the beach wedding, which had a country-chic theme and included fireworks and wish lanterns.
The couple had a busy lead-up to the ceremony that included applying for a marriage license, a wild bachelor party for the groom, who acted on Parenthood this year, and a rehearsal dinner on Monday night.
"@ElleSatine and I have been working our butts off, and now all we have to do is wake up, and get hitched!" Ritter, 29, Tweeted the night before they wed.
Ritter told PEOPLE that when he popped the question earlier this year, Satine cried. "I was shaking," he admitted. "And we were on a roof and no one fell off."
The singer has a busy few months ahead of him – he's just scored the lead role in the upcoming biopic Midnight Rider, playing the young Gregg Allman.