First-half goals from Callum McGregor and Olivier Ntcham at Hampden Park secured victory for Brendan Rodgers' all-conquering side.
The victory completed a second consecutive treble of Premiership, Scottish Cup and Scottish League Cup triumphs for the Glasgow giants.
Motherwell finished the league season 34 points behind the champions and they rarely looked like causing an upset.
A sumptuous half-volley from McGregor 11 minutes in set Celtic on their way, before Ntcham drilled home a second from the edge of the penalty area to put Rodgers' side in control.
Motherwell pushed hard as the second half wore on, with Gael Bigirimana rattling the crossbar from a free-kick, but Celtic deservedly held on to celebrate a slice of history.
"I'm so happy for everyone involved, players, staff, supporters," Rodgers told reporters after the game.
"It's an incredible achievement by everyone. I thought we thoroughly deserved it. A mention for Motherwell, they have had a great season."
The Bhoys planned to celebrate the historic achievement with an open-top bus parade through Glasgow from Dalmarnock Station to Celtic Park starting at 6.15 p.m. UK time.