Alexander Porfiryevich Borodin - other than being famous composer, he was also well known organic chemist, being among first to describe nucleophylic substitution and inventing aldol reaction.
When I was 15 or so, I was central repair hub for two dozens of musical groups, mostly in rock, punk or metal genres, taking care of their guitars/amplifiers/stomp boxes. In almost every group, there at least one member who was - or later became - electrical or mechanic engineer. None of those groups are known outside local circles, though, so I wouldn't call them famous. But anyway, there is a lot of EEs among musicians and a lot of musicians among EEs.