Mühlberger leaves German team Bora-Hansgrohe after five years, turning professional in 2016 and riding in six Grand Tours in that time including the last three instalments of the Tour de France as well as the Vuelta a España and Giro d'Italia.
In a statement on Movistar's website, the 26-year-old expressed his excitement at the prospect of chasing individual results and riding in support of the team's leading riders in bigger races.
Movistar's Enric Mas finished fifth overall at this year's Tour while Alejandro Valverde came in 12th.
"I'm super happy to have been given this chance by the team to sign with them and profit from all the opportunities that lie ahead in the next few years," Mühlberger said. "It's a good chance to improve my skills and get better in the future, chase some results on both the toughest one-day races and some mountainous one-week races like Dauphiné or Itzulia, but also try to help the leaders as much as I can in the Grand Tours."
"I feel like some of my best performances in previous seasons have come at the third week of Grand Tours, where I feel pretty strong, and I hope I can be there for our team leaders, put my current experience at the team's service and also learn a lot from the veterans, such as Alejandro Valverde, José Joaquín Rojas and many others.
Mühlberger acknowledged the move as a chance to further improve on his skills and grow his career in a new environment.
"There's still a lot for me to improve and learn, and I'm so happy to have this chance with the Movistar Team to grow with them and continue to get better in the next few years."
Team boss Eusebio Unzué welcomed the move, lauding the Austrian's multiple talents, experience and teamwork as valuable assets to Movistar going forward.
"Gregor's arrival will bring some extra experience to next year's team, thanks to his already vast experience in the WorldTour despite being still really young," Unzué said. "He's a polylvalent rider, something which is becoming increasingly important in modern cycling, and even if he's proven to be a great team rider, which is a big reinforcement in itself, I think he's more than qualified to lead the team in relevant events."