Jonathon Edwards, 21, was last seen at his Caernarfon home on 19 March.
His body was found on the Gwynedd mainland side of the water on Tuesday and his family has been informed.
His death is not being treated as suspicious and North West Wales coroner Dewi Pritchard-Jones has been informed.
A body found on the shoreline of the Menai Strait in north Wales has been identified as that of a missing man.