They were donated by Geraldine Menez, 83, whose great-grandfather, Henry Augustine Forse, was involved in remodelling the theatre in 1902.
The collection includes a rare "gold ticket", one of only two issued.
Along with Mr Forse's hand-drawn plans, they will be held by the University of Bristol Theatre Collection.
The collection, which is also home to the Bristol Old Vic Company Archive, already looks after five silver tickets.
Mr Forse, a builder, created the plans for the frontage of the theatre in 1902, parts of which were later demolished in the 1970s.
The university said it was Mr Forse's "passion for the theatre" which encouraged him to collect the four historic 'tickets', which were handed down through his family.
Ms Menez said: "I am giving the collection of silver tickets to the Theatre Collection in happy memory of 'the Gods'.
"My ancestors are like gods to me, as were the actors I beheld and listened to in awe at the Theatre Royal when I was younger on the frequent occasions I sat somewhere up in the dizzy heights just beneath the theatre ceiling on those hard, narrow wooden benches."
Jo Elsworth, director of the collection, said they were "delighted" such an important piece of Bristol's theatrical history has returned to its home city.
Money to build the original theatre came from 50 Bristol citizens who each pledged Â£50.
In return, they were given a numbered 'silver ticket' which granted the bearer the right to watch every performance in the theatre, forever - a benefit the theatre said it still offers today.
The two special "gold" tickets, which are actually made of silver, were given to Edward Crump and his wife Ann for the "great trouble and expense" they had gone to in order to persuade others to make over the land on which the theatre is built.
Unlike the silver tickets, their benefits were transferrable and could be used by others if they were lent them by the owners.
The Bristol Old Vic is currently fundraising to complete a major redevelopment of the theatre which it aims to start during its 250th anniversary next year.
Four of the original 'silver tickets' issued to the 50 supporters who helped fund the Bristol Old Vic theatre in 1766 have come home to the city.