The 27-year-old Landa will join Nairo Quintana and Alejandro Valverde for 2018 and 2019 after spending two seasons with Team Sky.
Landa represents the immediate Grand Tour future of Spanish cycling with Alberto Contador retiring at the end of the Vuelta a España and soon to be team-mate Valverde, now in his twilight years.
"It's great news for us," said Eusebio Unzue, the Movistar general manager. "Being still a young rider and with everything that he’s shown, he should be the rider who leads Spanish cycling for the next few years."
After a mixed first season with Sky, Landa revealed himself as a genuine Grand Tour contender in 2017 after claiming the mountains classification at the Giro d'Italia and producing a stellar ride at the Tour where he often appeared stronger than his team leader Froome. He then took the overall victory at the Vuelta a Burgos to continue his hot run of form.