Milne will begin immediately and help the firm expand its restructured digital media division.
He leaves behind his position as editor of Milne Media to take up the role.
Milne said: "Lucid is one of the best, brightest and boldest PR companies in the country right now and I’m hugely excited at taking on this brilliant new challenge."
Previously, he was editor of the Scottish TV network STV and was also consulting managing editor of national news agency Deadline News.
Lucid’s founder, Peter Kane, said: "We are delighted Shaun is joining our experienced team. His knowledge and expertise will significantly enhance the service we offer to clients, especially in digital media."
The move will allow Kane to head up the recently formed Neptis Group, a merger between Lucid and Glasgow-based Vitel earlier this year.