Julian Carnell, from the trust, said the park was "one of the English Riviera's crown jewels" and it was a "once in a generation opportunity for Cockington".
Dogs are believed to be responsible for the deaths at Cockington Country Park and visitors have been asked to keep a lookout for any animals not under control.
Torbay's share, which followed a bid by Torbay Development Agency, will support the development of start-up businesses, social enterprises and an apprenticeship scheme and a new cycle route around Cockington.