The 86-year-old actor, who featured in Hollywood's iconic sci-fi franchise as Captain James T Kirk, took to Twitter to pay homage to the late star.
"Remembering a dear friend who was born today," wrote Shatner alongside an old picture of him and Nimoy where the two can be seen hugging each other.
Nimoy was renowned for playing the half-human, half-Vulcan character, blessed with a level-headed and logical outlook, Spock.
He went on to essay the role from the first 1966 TV episode to the film, "Star Trek Into Darkness" in the year 2013, which was also his final performance.
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