O'Brien played for Ireland in their Grand Slam-winning team of 1948 and later managed the Lions on their 1966 tour of Canada, Australia and New Zealand.
The former back row forward died at his home near Edinburgh on Christmas Day, the Irish Rugby Football Union announced.
IRFU president Andy Crawford said: "The IRFU would like to pass on its deepest sympathies to Des O'Brien's family at his recent passing.
"Des served both Ireland and his club with great distinction and he will be sorely missed by his past team-mates and his friends.
"His name will remain synonymous with the 1948 Grand Slam, but his services to the game went beyond his first international season, where he went on to captain Ireland and manage the British & Irish Lions. May he rest in peace."
O'Brien won 20 Ireland caps, played in a number of matches for which caps were not awarded, and was ever present from 1948 to 1952.
The Edinburgh area was his adopted home, and a statement from Scottish Rugby expressed the body's "sincere sympathies to family and friends" of O'Brien.