Hooper netted after eight minutes when Hibs failed to clear a low Mikael Lustig delivery and Anthony Stokes took Ben Williams out of play with a deep curling return cross to the back post where his fellow striker arrived between two defenders to volley into the net.
And Hooper was on target again (31) when Stokes delivered another swirling ball to the back stick and Celtic's top scorer arrived between Paul Hanlon and Ryan McGivern once more to head into the far corner past the exposed Williams.
Hooper could have completed his treble 10 minutes from time but he mis-hit from close range after Stokes and Lustig combined to open up the Hibs defence, and when the ball broke to Ledley the Celtic midfielder rifled into the top corner.
Hibs twice threatened to break the deadlock in the opening exchanges with a dipping Tom Taiwo shot from 25 yards and a close-range header from Eoin Doyle which forced Fraser Forster into a brilliant diving save.
In between Hooper's goals, Stokes sent a low shot into the side-netting before a quick Kris Commons pass put Ledley clear in the box but the midfielder shot straight at the advancing Williams.
Leigh Griffiths almost got Hibs back into the game just before the break when he latched onto a long diagonal pass from Hanlon but the striker was forced wide by Forster to cut off the angle for a finish and Lustig shepherded the ball across the six-yard box.
Hibs refused to buckle though and battled gamely after the break despite being unable to create any chances by a resolute Celtic defence, but a comeback akin to the semi-final heroics was beyond Pat Fenlon's men on this occasion.