The window featuring a distinctive red cockerel, survived Henry VIII's dissolution of the monasteries and lay discarded but unbroken in rubble for centuries.
English Heritage will unveil the ten centimetre square fragment at Rievaulx Abbey, near Helmsley, on Tuesday.
It is the only one of 8,500 glass pieces recovered from the site that depicts an entire animal and is the most complete piece ever found at the 900-year-old ruins.
Animal motif
The piece was rediscovered in a collection at English Heritage's Central Science Laboratory in Portsmouth.
Senior curator Andrew Morrison said: "This really is an exciting rediscovery.
"We've never found anything as good as this fragment before, bearing a complete animal motif.
"It appears it came from the east end of the Abbey church, which was built to house the shrine of Rievaulx's most famous abbot St Aelred."