The new scheme is sponsored by PwC and will replace the existing Under-25s club discount.
"We are delighted to continue our relationship with The Old Vic and to further develop it by offering PwC £10 Previews," said Ian Powell, chairman and senior partner at PwC.
"Working together, we will help to ensure that the theatre is made even more accessible and inspiring to a wider audience."
Matthew Warchus, The Old Vic artistic director designate, said: "My ambition is to make the artistic popular and the popular artistic, and, with the invaluable support of PwC, we will be able to launch a new ticketing scheme, the PwC £10 Previews, which will make our shows more accessible and affordable for all.
"Whether you're young or old, we aspire to offer you something that will appeal. I firmly believe in the overwhelming and transformative power of live performance, and we are delighted to be partnering with PwC to inspire a new audience at The Old Vic."
The new scheme begins in September.