His club boss Walter Smith was also honoured, receiving Manager of the Year honours at the awards ceremony held at Glasgow's Kelvingrove Art Gallery.
Cuellar's honour came as no surprise, and he could follow it up by landing the PFA Scotland award on Sunday, and the Scottish Football Writers' Association prize next month.
His team are on course to end Celtic's reign as Scottish champions after two league titles in succession for Gordon Strachan's side.
MAIN AWARD WINNERS
Manager of the Season - Walter Smith (Rangers)
Under-19 League Player of the Season - Scott Anson (Kilmarnock)