The former Scunthorpe striker bagged two goals at Hampden Park as the Glasgow club inflicted a second-consecutive Scottish Cup final defeat upon their opponents
The defeat is the Edinburgh side's second-successive cup final loss, after they fell at the hands of local rivals Hearts in 2012, and sees their barren stretch in the tournament continue, having failed to lift the trophy since 1902.
Hibernian boss Pat Fenlon was without skipper James McPake, who failed a fitness test last week, which meant a cup final place for 19-year-old defender Jordan Forster, who made his debut in the Edinburgh derby two weeks ago, while Leigh Griffiths shook off an injury scare to lead the attack.
His opposite number Neil Lennon went for his strongest possible side after wrapping up the SPL title with time to spare, which meant he could hand starts to Charlie Mulgrew and Anthony Stokes, while Efe Ambrose and Georgios Samaras were forced to settle for a place on the bench.
The Edinburgh side caused most problems early on and, with six minutes gone, on-loan Manchester City defender Ryan McGivern managed to get a cross in from the left, but Eoin Doyle's header was well saved by Fraser Forster.
Hibernian were made to pay for that a couple of minutes later as Stokes picked the ball up on the left and delivered a cross to the back post, which Hooper had no trouble diverting past Ben Williams and into the net.
The Celtic onslaught continued thereafter, as Ledley managed to get in behind the Hibernian defence to latch on to a pass from Kris Commons, but Williams cleared the ball with his legs in order to prevent his side from going further behind.
On the half-hour mark, though, Lennon's side did double their lead as Stokes found space on the left and whipped the ball across the penalty area to leave Hooper with the simplest of tasks in heading home.
After the half-time break, the Easter Road side came out with a new level of determination as young winger Alex Harris played the ball into the danger area in search of Griffiths, but the Scotland call-up got the ball caught between his feet and Celtic eventually cleared.
Hibernian continued to press forward, but they couldn't find a way past Forster in the Celtic goal and Griffiths continued to look like an isolated figure in attack.
With 12 minutes remaining Celtic secured the Scottish Cup as Mikael Lustig was allowed the freedom of the right wing to cross into the box. Fortunately for the Hoops, after Hooper missed the initial effort, Ledley was there to fire home from just inside the box.
That ultimately saw Hibernian's dream of lifting the Scottish Cup come to end and sees their hoodoo in the competition stretch to 112 years.