The decision from the European Court of Human Rights said the passage of time did not erase Turkey's responsibility in the case, ruling that Turkey must pay 30 million euros in damages to relatives of those missing in the operations and 60 million euros for "the enclaved Greek-Cypriot residents of the Karpas peninsula."
Hundreds of Greek Cypriots still live in the Karpas peninsula in the northernmost tip of the breakaway Turkish Cypriot part of the island.
Cyprus has been divided since Turkey invaded after a coup by supporters of union with Greece. Only Turkey recognizes the breakaway Turkish Cypriot state that was proclaimed in the north of the island.
The judgment comes as the Turkish and Greek Cypriot communities are making a new effort to reunite the island.
The court said it would be up to the government of Cyprus to determine how to award the damages. Turkey has not always complied with the court's rulings.
In a 1998 ruling, the Strasbourg court ordered Turkey to pay Titina Loizidou 1.2 million euros ($1.4 million) in compensation for depriving her of property in the seaside city of Kyrenia. It was the first case in which a Greek Cypriot successfully sued Turkey over the invasion and earned the right to compensation.
Turkey paid the money in 2003, but has yet to comply with an earlier European Court decision ordering Ankara to allow Loizidou to reclaim her property.
Angela Charlton and Lori Hinnant contributed from Paris.