The 22-year-old was initially diagnosed with testicular cancer towards the end of December, and underwent an operation to remove the tumour.
The full-back, who made an emotional return to the field in February's La Liga clash with Barcelona, was then handed a fresh contract at San Mames after recovering from the illness.
However, Bilbao revealed in June that checks picked up 'an abnormality', meaning that Alvarez would be forced to undergo a new course of treatment.
Alvarez's latest course of chemotherapy appears to have been a success, with Bilbao revealing that "the disease has ended".
"The treatment phase scheduled in June for the disease has ended," read a statement from Bilbao. "In the next few days [Yeray] will be discharged and will begin the phase of progressive incorporation to the team. At the same time, an active surveillance program will be planned."
Alvarez came through the youth system at San Mames, representing the club's second team before earning promotion to the senior set-up ahead of the start of the 2016-17 campaign.