The Glasgow side took control after South Korean midfielder Ki Sung-Yeung lashed in from 30 yards after 32 minutes in a contest played in driving rain.
Motherwell, in the final for the first time since their 1991 triumph, hit the bar through Gavin Gunning but two goals in the final 15 minutes ended their hopes.
Marc Wilson's low shot clipped Motherwell defender Stephen Craigan and wrongfooted keeper Darren Randolph and Charlie Mulgrew sealed Celtic's triumph with a well-struck free-kick.
It was Celtic's 35th Scottish Cup triumph and their first silverware under manager Neil Lennon, who has endured a troubled season.
Lennon was attacked by a man during his team's match against Hearts in Edinburgh earlier this month, while last month parcel bombs sent to Lennon and two high-profile Celtic supporters were intercepted by police.
These incidents have been the latest in a succession of problems for the former Northern Ireland and Celtic captain who previously received death threats, leading him to prematurely retire from international football.
On the pitch, his side suffered a surprise 3-2 defeat to Inverness earlier this month which all but handed the league title to their city rivals. But Saturday's victory enabled Lennon and his side to end the season on a high.
