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28 July 2015 Last updated at 21:39 BST
The ships were destroyed during storms in 1588, and more than four centuries later, a man walking along the County Sligo coast found a washed-up piece of timber that turned out to be a rudder from one of the wrecks.
The cannon are now being treated at the National Museum in Dublin where it is hoped they will eventually go on public display.
BBC Newsline's Dublin correspondent Shane Harrison reports.
A chance discovery during storms along the west coast of Ireland earlier this year has led to nine Spanish Armada cannon being recovered from shipwrecks.