Burke was presented by Alaves on Wednesday following his loan switch.
The Scotland international will wear the No.24 shirt for Asier Garitano's side with whom he has already completed three training sessions.
"It's a great opportunity for be to be able to sign for Alaves," he stated.
"I am very happy. The club has made me feel very welcome from day one," he added.
Burke stated that he was compared with Gareth Bale when he was younger but wants to create his own merits.
"When I was younger there would always be comparisons with older players. They used to compare me to Gareth Bale but he is on another level.