Martin O'Neill's side swept into a two-goal lead before half-time thanks to goals from Daizen Maeda and Arne Engels at Hampden Park.
Kelechi Iheanacho struck after the interval to put the result beyond doubt, making Josh Cooper's late reply little consolation for out-classed Dunfermline.
It was a ninth consecutive win in all competitions for Celtic, who have timed their best run of form perfectly after being galvanised by interim boss O'Neill.
Celtic's 43rd Scottish Cup success capped an incredible end to the season for O'Neill.
The 74-year-old now has nine major honours as a Celtic manager stretching over 26 years.
It was Celtic's 14th top-flight and Scottish Cup double.
O'Neill is in his second spell as caretaker boss of the Glasgow club this season and is yet to agree to return next term.
So it was fitting that O'Neill's potential farewell came in against Dunfermline boss Neil Lennon, who was a key member of O'Neill's Celtic and Leicester teams earlier in his managerial career.
Asked if he could be persuaded to stay, O'Neill said: "Next week I might get to speak to the owner. Dermot Desmond brought me back in the first place, I owe him a great deal otherwise I wouldn't be here.
"If the season was to start tomorrow, I couldn't do it. But the season doesn't start tomorrow. The Scottish season does start quickly though, and I'm getting old.
"What I have is a passion for the game. I don't think that will ever leave me, even in my final days. That's always been me. I have a desire to win."
Celtic pipped Hearts to the Scottish Premiership title last weekend, coming from behind to win 3-1 against the Edinburgh club on the final day of the season.
The Hoops needed late goals from Maeda and Callum Osmand to finish two points above Derek McInnes' side, who had led the table for months.
Hearts were furious that Celtic had stayed in the title race with a helping hand from a debatable penalty that clinched a win at Motherwell in their penultimate game.
There was, however, no need for any contentious drama in the final.
Celtic took the lead in the 19th minute as Alistair Johnston's ball reached Maeda and he lobbed it over the stranded Aston Oxborough.
They doubled their advantage in the 36th minute when Engels hit a powerful strike from 25 yards that left Oxborough flat-footed.
Iheanacho latched on to Benjamin Nygren's through ball and showed tremendous footwork to evade three defenders before slotting home in the 72nd minute.
Cooper scored on the rebound after Charlie Gilmour's shot had been blocked in the 79th minute, but Celtic were never in danger of surrendering their lead.