The head of an 800-year-old mummy known as The Crusader was stolen, along with another skull, from St Michan's Church in February.
The vault has been closed to the public since it was vandalised.
It was badly damaged and several of the mummies, including the 400-year-old remains of a nun, were desecrated.
The Crusader's body was turned over and his head removed. Some of his bones were scattered outside the coffin.
Archbishop Michael Jackson and Archbishop Diarmuid Martin visited the crypt following the break-in and appealed to those responsible to examine their consciences.
The mummified head and the skull were recovered by gardai, from Bridewell garda station, in March, and a 35-year old man was charged.
Since then, specialists from the National Museum have been restoring the skulls.
A local undertaker made new coffins for the mummified remains and security has been increased in a bid to prevent any further break-ins.
The crypt had been previously targeted by vandals in 1996.
It will re-open to the public on Tuesday.
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