The works, thought to have been written for amateur musicians, were found in a 180-page portfolio after it was donated to the Foundling Museum in London.
One of the rediscovered compositions will be performed at Liverpool Hope University on Sunday.
It is likely to be its first airing in the modern era, the university said.
The anthology of manuscripts was compiled between 1715 and 1725, with Vivaldi’s sonatas filed alongside works by Handel, Corelli and Purcell.
It was acquired by the late businessman Gerald Coke, whose collection was handed to the Foundling Museum in 2008.