Gompertz, who joined this week in a part-time capacity, takes on the role full-time from next April.
He replaces Sophie Ahrowes, who left the post, then called head of marketing and communications, to return to freelance consultancy work.
As director of comms Gompertz will oversee the central 16-strong corporate communciations team and press officers dealing with the Tate Modern and Tate Britain.
PR staff in the two other galleries, in St Ives, which opened in 1993 and in Liverpool, which opened in 1988, do not report directly to Gompertz, but he will offer advice on their communications strategy.
Gomertz joins from visual arts magazine Zoo, which he founded and for which he acted as publisher and editorial director. He also founded the magazine Shots, which is now owned by Emap.
Gompertz reports to deputy Tate director Alex Beard, who said Gompertz was hired on the strength of his knowledge of the advertising and visual arts sector.
Tate PRO Nadine Thompson said two major PR projects Gompertz will oversee are the marketing and publicity for the forthcoming Tate Modern exhibition of Max Beckmann works, and the Tate Britain's Constable to Delacroix season, both starting in February.
Prior to Harrowes taking the post, the top PR role at the Tate was held by Damien Whitmore, now public affairs director at the Victoria & Albert Museum (PRWeek 16 November, 2001).