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The eight-time Olympic athletics champion and world record holder in the 100m and 200m announced the children's birth on Instagram to mark Father's Day.
Bennett added in a separate post that the sprinter was "the rock of this family and the greatest daddy to our little ones".
However, neither Bolt nor Bennett confirmed when the twins had been born.
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Bolt, a Jamaican sprinting icon, retired from athletics in 2017 and still holds the 100m and 200m world records, making him the fastest man in history.
He is also the only man to have won three 100m Olympic titles and 23 major gold medals during his career.