The Irish side became the first team outside of England and France to combine domestic glory with the continent's top honour by overcoming the defending champion, which beat Leinster in the semi-finals en route to last year's crown, in a thrilling encounter.
Leinster controlled possession for long periods and proved too good for the Scarlets, who suffered a repeat of their Champions Cup defeat to the same team last month despite a hat-trick from Johnny McNicholl.
Johnny Sexton proved integral on his comeback from a calf injury, creating tries for James Lowe and Sean Cronin before being replaced by Joey Carbery in the 64th minute, while Jordan Larmour scored a sensational solo effort in an impressive win.
Despite Leinster skipper Isa Nacewa being forced off in his final match before retirement, the hosts got the first try in the 30th minute when Devin Toner crashed over after 23 phases of play.
The Scarlets hit back quickly, though. McNicholl — playing on the wing with Leigh Halfpenny slotting in at full-back on his return from a hamstring injury — broke the Leinster line and, after Steff Evans and Gareth Davies fell short, picked the ball up from the ruck to dot down.
Sexton showed quick hands to send Lowe over in the corner with virtually the last act of the first half, before a pinpoint kick after the Scarlets were penalised for a high shot resulted in Cronin crossing.
Larmour made it two in six minutes when, running out of space on the right, he chased his own kick down the wing to send the stadium into raptures.
An acrobatic second from McNicholl gave the Scarlets hope, but some superb footwork from Luke McGrath created space in the visitors' line and Jake Conan dived beneath the posts.
Werner Kruger touched down for the Scarlets and McNicholl completed his trio with the final play after a stunning run from Scott Williams in his last outing before moving to the Ospreys, but it proved insufficient to retain their title.