It was announced in January that Hornby would be taking a break from the soap because of ill health.
He originally signed a three month contract with the soap - but he ended up staying in the Dales for 28 years, making him the soap's longest-serving cast member.
Emmerdale series producer Anita Turner said she was "deeply saddened" by "a devastating loss".
She added, "He was a hugely popular and well-respected member of cast and a terrific actor."