The judgement is one of the largest ever ordered by the court.
It said the damages were compensation for losses endured during the invasion and in the subsequent partition.
Cyprus has been divided since 1974 when Turkey invaded the north in response to a military coup on the island which was backed by the government of Greece.
Since then, the northern third has been mainly inhabited by Turkish Cypriots and the southern two-thirds by Greek Cypriots. Turkey still has around 30,000 troops stationed on the island, and it is the only country that recognizes northern Cyprus as a separate entity.
UN peacekeeping forces estimate that 165,000 Greek Cypriots fled or were expelled from the north, and 45,000 Turkish Cypriots from the south, although the parties to the conflict say the figures are higher.
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