The decision ends weeks of tension over a dispute with the recently elected president of the Football Federation of Chile (ANFP).
Last week Sampaoli said he "felt like a hostage" after Jadue's successor, Arturo Salah, refused to reduce an exit clause in his contract.
Fazio said Sampaoli, an Argentine, would lose bonus money from winning the South American championship and would also have to pay a portion of any new contract to the Chilean federation.
Jorge Sampaoli has stepped down as Chile coach which in turn has sparked speculation about possible links to Chelsea in the summer.
He took over the reins of the national team in 2013.
Aside from qualification for the 2018 World Cup, Chile are also preparing to defend their title at the Copa Centenario in the United States later this year.
Former Argentina and Chile coach Marcelo Bielsa and current Celta Vigo coach and Bielsa's former assistant Eduardo Berizzo are likely candidates to take Sampaoli's post, local media reported.
"I hope to remain with competitive teams in Europe, I am not thinking about returning to Chile at least for the next three or four years", the veteran manager told Radio Cooperativa.
"There is no chance I would coach over the next couple of years".
Sampaoli was nominated for the FIFA Men's Football Coach of the Year award at last week's FIFA Ballon d'Or Gala in Zurich, an event he attended. "But being in charge of the national team is not something I would like to do at this time".
