The parties have agreed to a purchase price of 200 million euro ($244.7 million), subject to certain closing conditions and a minimum purchase price of 50 million euro, Advent International said in a statement.
Under the terms of the agreement, Advent International will acquire 80% of SEE-Network, with the EBRD taking a 20% minority stake.
Hypo's network of subsidiary banks and leasing companies in Bosnia and Herzegovina, Croatia, Montenegro, Serbia and Slovenia have been hived off as part of an orderly wind-down agreed with the European Commission.
"We want to develop this banking group into a strong and profitable service provider that is dedicated to serving retail and SME clients in the region [..]," Christian Stoffel, director at Advent International in Frankfurt, said.
For his part, Nick Tesseyman, EBRD managing director financial institutions, said the transaction gives the SEE Network a fresh start. "We are dedicated to the long-term development of SEE Networks's core markets and we will help grow this banking group into a stable first-class financial service provider in the region."
Buyer and seller have agreed to terms that allow for a repayment schedule for approximately 2.2 billion euro of existing credit lines, half of which will be in the form of secured credit lines.
Since 2009, Hypo Alpe-Adria Bank International AG/Heta Asset Resolution has been wholly owned by the Austrian government.
Advent International intends to maintain the banking group's operations under a holding company based in Austria and operating under an Austrian-banking license.
In particular, Advent plans to revitalise and grow the bank's retail and SME service offering in its core regions, the statement said.
The transaction, subject to a number of closing conditions such as customary approvals of the European Commission and the relevant regulatory authorities, is expected to close in mid-2015.
Hypo has 245 branches and around 1.15 million clients in SEE with total balance sheet assets of around 8.4 billion euro.
($=0.8175 euro)