It will be the first time the two teams have met outside Wales, but won't be the first time that Wales has played an international at the home of Bristol City FC.
They met England there in 1908 on 18 January in a match marred by fog, with Wales winning 28-18. The WRU also staged the 1998 Swalec Cup final at the Bristol venue when the Millennium Stadium was being built, Llanelli defeating Ebbw Vale 19-12.
"We have enjoyed three great games against the Barbarians in the last three years at the Millennium Stadium and we are delighted that they have offered us this chance to meet them again," said WRU general manager Steve Lewis.
"When our three year agreement came to an end last season we made them aware that the Millennium Stadium would not be available at the end of May in 2004 because of other commitments. However, the Barbarians decided they still wanted to play us and offered us the chance to travel to meet them at Bristol.
"After discussing the matter with the Wales team management, it was agreed that it would be an excellent fixture for the Welsh squad to undertake before they depart on their three-test summer tour of Argentina and South Africa."
The Millennium Stadium is unavailable for use on 26 May because of the existing contract that is in place with the Football League to host the Nationwide League Play-Off matches at the end of that week.