The 28-year-old was a virtual ever-present for the Canary Island outfit last season making over 30 appearances in La Liga.
Alonso has signed a three-year contract with the Estadio Mendizorroza club, having played for Las Palmas for the past two seasons.
The midfielder becomes the third major summer signing following the arrivals of Barcelona duo Abelardo and Richard Dutruel.
Meanwhile, the club have denied they are interested in signing Spanish international midfielder Albert Celades from Real Madrid.
The 21-year-old former Celta Vigo and Barca star has found holding down a first-team place at Santiago Bernabeu hard to come by, with stars such as Zinedine Zidane, Claude Makelele, and Flavio Conceicao in the midfield, and is rumoured to want to leave the Madrid giants.
