The 32-year-old signed for the British team in 2016 after five seasons with Movistar, during which he won two stages at the Giro d'Italia and the Tour of Beijing, but has only raced 22 days since then.
He was diagnosed with mononucleosis in early 2016 and has struggled to rid himself of the virus. After 15 race days in 2016, he made his 2017 debut at the Clasica San Sebastián in late July but did not finish, and his only other appearance that year was at the Tour of Guangxi in October, where he abandoned on the second day.
Despite his illness woes, Team Sky gave Intxausti another year on his contract for 2018, but the hoped-for recovery did not materialise. He abandoned the Tour of Norway on the opening day in May and, although he completed the Norwegian round of the Hammer Series soon after, his only other appearance was a DNF at Cyclassics Hamburg in August.
"Now I feel well and I'm looking to the future," Intxausti said in a statement announcing his move to Euskadi-Murias.
The Pro Continental team have a strong Basque identity - though they do not exclusively hire Basque riders - and Intxausti, who hails from Bizkaia and spent a year with the old all-Basque Euskaltel-Euskadi squad, will fit in in that respect.
"I believe in this project, it's our project, the leading project in Basque cycling which is laying good foundations for the future and is always thinking about nurturing home-grown talent," said Intxausti. "The team has established itself little by little, above all in the 2018 season with some big results. That's why I'm joining this team."
Team manager Jon Odriozola, who steered the team to the Pro Conti ranks and saw them win a stage in their debut Vuelta a España, believes Intxausti can finally overcome his health issues this winter and enhance the squad in 2019.
"For us it's a very big thing to have Beñat Intxausti next year," he said. "He is among the best Basque riders and, although he has had a couple of bad years, we want to get him better and achieve great things with him."