The French side ran out 25-17 winners to claim their first European Cup final success at the fifth time of asking.
Jonny May had opened the scoring against the run of play following an interception but Sergio Parisse’s try helped Stade level in the 32nd minute.
Gloucester survived a yellow card for scrum-half Willi Heinz but the French side increased their domination in the second-half and tries from centres Jonathan Danty and Geoffrey Doumayrou earned them victory, with Ross Moriarty’s late reply only a consolation.
Gloucester stunned their opponents in the 14th minute when May intercepted a move down the Parisians’ right side and ran almost 70 metres to go over.
Billy Burns added a conversion and soon another three points after some brilliant footwork from Tom Marshall had put the Top 14 side on the back foot.
May stopped a promising break but the Top 14 side kept up the pressure and Jules Plisson got them off the mark with a 45-metre penalty.
Plisson then set up their first try with a dink towards the line. Hugh Pyle managed to palm the ball back into the path of Parisse and the Italian touched down..
Gloucester were guilty of over-playing moments later inside their own half and Camara intercepted before Bonneval fed Danty to go over the line.
Plisson could not convert but Stade continued to spend the game in the Gloucester half and Doumayrou side-stepped and shimmied his way through the Gloucester defence to score before Morne Steyn added five more points with the boot.
It was painful viewing for the Gloucester fans but there was some respite when Moriarty burst through to cross in the 79th minute on a rare attack.
Marshall, Sharples, Scott, Atkinson, May, Burns, Heinz, Hohneck, Hibbard, Afoa, Savage, Thrush, Moriarty, Ludlow, Morgan.
Twelvetrees for Scott (62), Trinder for Atkinson (72), Laidlaw for Heinz (43), Y. Thomas for Hohneck (63), Dawidiuk for Hibbard (73), Galarza for Savage (60), Clarke for Thrush (75).
Bonneval, Nayacalevu, Doumayrou, Danty, Camara, Plisson, Genia, van der Merwe, Bonfils, Slimani, Pyle, Gabrillagues, Burban, Ross, Parisse.
Sinzelle for Danty (73), Steyn for Plisson (67), Panis for Bonfils (73), Alo-Emile for Slimani (41), Alberts for Pyle (67), Lakafia for Burban (59).
John Lacey (Ireland).