Number eight Parisse's international team-mate Martin Castrogiovanni, a prop, was also named along with Samoan scrum-half Kahn Fotuali'i and France back-rower Imanol Harinordoquy.
Fourie scored a late try for South Africa in the second test defeat of the Lions in Pretoria in 2009 to help secure the series for the hosts.
The Barbarians, who will be coached by three-times Lions tourist Dai Young, will play England at Twickenham on May 26 before departing for the Lions encounter in Hong Kong on June 1.
"This year's summer tour is a very important one for our club," said team manager Derek Quinnell.
"It is a great honour to play the Lions as well as England and we are very conscious of the need to invite the strongest possible squad to do justice to two great fixtures."
The Lions will play three matches against the Wallabies in June and July in their quest to win a first Test series since 1997.
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