Cuellar, 27 later this month, will put pen to paper on a £7.8m deal after Rangers were forced to accept a bid.
The former Osasuna man had a clause in his contract, which was activated by Villa's bid.
Rangers fans are understandably disappointed as Cuellar was named as SPL Player of the Year last season.
Villa messageboards have been flooded with messages wishing Cuellar well in the Midlands.
The centre back, affectionately known as 'Ugly Betty' by fans of the Glasgow giants, played a huge part in the club reaching the UEFA Cup Final.
Although Rangers eventually lost to an Andrei Arshavin inspired Zenit St Petersburg in the Manchester showpiece, Cuellar's reputation was enhanced.
The Madrid born hardman has the traits to cope with English football and may already have the inside track on Villa as he trained alongside Savo Milosevic at Osasuna.
Savo didn't exactly leave with his head held high, but Cuellar enters with just that. Villa Park expects!