The 26 year old Spaniard had already been named Scottish Premier League and Scottish Football Writers' Association player of the year.
"It was fantastic to be voted the player of the year for Scotland and to be voted for by the Rangers' fans is special too," he told the club's website.
Boss Walter Smith hailed Cuellar as a "fully deserving" recipient.
"Carlos has been a terrific signing for us," he said.
"I think he came to us at the right time in his career and he has played exceptionally well for us both domestically and in Europe.
"Sometimes it's easier for players who come from abroad to show up better in the European matches because the SPL games are different to what they are used to.
"But Carlos has handled both with great aplomb and he is fully deserving of his awards."