The couple were spotted on a beach in Long Island, N.Y., and dressed down for the occasion in shorts, T-shirts, sneakers and sunglasses.
"Year one, done," Paltrow, 47, captioned a beaming selfie with producer Falchuk, 48, on Sunday.
Falchuk and Paltrow made headlines in June when the Oscar-winner revealed they didn't live together at the time.
Paltrow explained that dividing the space has been healthy for their relationship and even noted that her married friends say “the way we live sounds ideal.”
Falchuk added that Paltrow is much better than he is at brushing off the criticism about their space-sharing scenario.
"There’s a media version of her and me, but we’re just home cooking dinner. Or she’s just cooking me breakfast. That’s all. We could not be a more normal couple…Gwyneth has a very tough skin. She’s like, ‘You’ve got to relax.’ At the end of the day, we’re getting into bed together…and nothing from the outside world or anybody’s opinion means anything," he said.
In an interview with InStyle, Paltrow said that "married life has been really good."
She added, "I adore my husband. He’s brilliant and deeply kind. I feel like he’s a real equal, too. And he pushes me in the best ways. I really like being married. It’s fun."
Falchuk revealed in August that they planned on moving in together this month.
Fox News' Tyler McCarthy and Jessica Napoli contributed to this report.