"So happy to spend my life with you," the former Agents of S.H.I.E.L.D. star wrote, adding the hashtags "#ido" and "#iloveyou."
Palicki stars as USS Orville First Officer Kelly Grayson on the fan-favorite FOX comedy from creator and co-star Seth MacFarlane, who plays Kelly's ex-husband, Captain Ed Mercer. Grimes portrays Lieutenant Gordon Malloy, a role penned specifically for him by longtime friend MacFarlane.
Palicki was previously engaged to Captain America: Civil War and Avengers: Infinity War stuntman Jackson Spidell, but that relationship ended before the two could marry. Grimes has been married twice, first to Dawn Bailey and then Megan Moore, both marriages ending in divorce.
The Orville, now in its second season, sees Kelly and Ed's relationship "take a new turn, while the ship's crew will meet never-before-seen aliens, face old adversaries the Krill, make first contact with a new civilization and revisit the planet Moclus," per its official synopsis, with Jessica Szohr and Chris Johnson on board as the series' newest stars.
Palicki recently teased the season will soon bring "a huge storyline" for Kelly, culminating in "kind of a two-parter, at the end of the season," she told TV Line.
"It was one of the hardest acting experiences of my life but really fun, and hopefully people love it as much as they loved that episode last year. And no, I can't tell you about it."
As its sophomore season nears its end, FOX is already eligible for a California tax credit should Orville be renewed for its third season.
"Well, that's the thing about Season 1 — you kind of figure out what works and what doesn't, and the nice thing is that the fans were just, like, overwhelmingly excited about everything we did last season," Palicki said.
"But this year, we've stepped up our game a bit. I think that every episode kind of feels like a miniature movie. There's going to be more delving into relationships with different characters on the ship and that is going to evolve some characters. It's not just going to be about a ship going on these adventures; you're going to finally get to see underneath."
The Orville airs Thursdays at 9 pm on FOX.