Chairman of Chime's PR businesses Kevin Murray this week confirmed Frohlich has been recruited to assist Chime chairman Lord Bell and himself on "a new string to our bow", but declined to give any details.
It has also been announced this week that Frohlich, who joins later this month, will take associate director Graham Drew with him to Chime.
It is understood job titles for the pair are yet to be decided.
Frohlich joined Shine from Bell Pottinger in 1999 as associate director, replacing co-founder Rachel Bell, who became chairman. He was promoted to MD a year ago.
Drew joined around three-and-a-half years ago as an account manager.
Rachel Bell, who will revert to her former role as MD when Frohlich leaves this Friday, stressed the departure was amicable.
She said Shine had "perhaps become a bit top-heavy", and the departures could "create opportunities" for other staff to progress to board-level status.
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