The Navarrese side have won twice in LaLiga and sit 16th in the table with eight points. A ragged 5-2 defeat by Real Betis on Sunday was Ramis' final chance to prove he was the right person for the job.
Arrasate has signed a contract until 2029. The 48-year-old returns to El Sadar after a two-year gap, during which he managed at Mallorca.
Vicente Moreno, Alessio Lisci and Ramis all had spells as manager after Arrasate, but none lasted more than a season. Ramis took the reins in July, but a run of four defeats in five, conceding 17 goals, ended his tenure.
In his first six-year stint at Osasuna, Arrasate became a hero in Pamplona, guiding them back to LaLiga and taking Osasuna to a second Copa del Rey final appearance in their history in 2023. They qualified for the Conference League in the same season.