Separately, Capelight Films has taken the German rights.
The New Zealand feature, a comedy about two misfits starring Loren Horsley and Jemaine Clement, premiered at Sundance before playing in Rotterdam and Berlin.
Ainsley Gardiner and Cliff Curtis of Whenua Films produced the film, which was backed by the NZ Film Commission and Unison Films.
The UK deal was negotiated by Optimum's managing director Will Clarke with NZ Film's head of sales & marketing Kathleen Drumm and business affairs executive James Thompson.
Miramax has already taken North American rights and plans a June 15 release. Icon has Australian and New Zealand rights, with Hoyts handling the New Zealand release.
'We are delighted to be releasing Eagle Vs Shark in cinemas in the UK - the British public love to discover new talent and Taika is certainly talented. He has crafted a film that is truly original and hilarious. We're going to have lots of fun working on it,' said Danny Perkins, Optimum's head of distribution.