Geldof will become a non-executive director of the new £9m company, which is to be called Ten Alps Communications.
Under the terms of the all-share deal, Osprey will raise £3.4m through a share placing at 23p and reverse into Ten Alps and its sister company Instant Party.
News of the takeover was first reported in early June when shares in Osprey were suspended amid speculation that the AIM-listed company was in talks with Ten Alps.
Osprey is headquartered in London, with offices in Edinburgh, Southampton and Belfast. Osprey was acquired by the Interfocus Group in September. Interfocus itself is majority owned by Canadian communications Maxxcom.
Ten Alps produces shows for the BBC, among others, including Radio 5 Live's Sunday Service programme.
Geldof said, "We do TV, radio and events production. By adding advertising and sponsorship revenues, it allows us to own that content which, in the world of new media, is the name of the game.
Last year, Osprey narrowed its pre-tax loss from £1.3m in the previous period to £129,000 on sales down £16m to £9m.
The takeover has to be agreed by Osprey shareholders at an EGM, which will take place on July 27.