Eden Hazard, who all but confirmed his Chelsea exit post-game, netted twice while Olivier Giroud and Pedro also scored in the emphatic win.
Scores were locked 0-0 at the break before Giroud put the Blues ahead against his former club in the 49th minute.
Pedro doubled Chelsea’s lead in the 60th minute with Hazard adding another from the penalty spot five minutes later.
Arsenal substitute Alex Iwobi fired in the goal of the game in the 69th minute to give the Gunners some hope, but Hazard settled the result three minutes later.
‘‘I think both teams were playing with a bit of stress with it being a final but when Olivier scored it was the beginning of a great night,’’ Hazard told BT Sport.
‘‘We played well and controlled the game and I’m happy to leave this trophy with the boys.
“The manager said to carry on playing football at the break and today we showed this mentality.’’
The triumph is Chelsea’s third European trophy in the past decade and their first piece of silverware under Maurizio Sarri.
Meanwhile, Arsenal haven’t lifted any European silverware since their 1994 Cup Winners’ Cup triumph.
Gunners boss Unai Emery said: “Chelsea deserved to win. We got to the box with good options and chances to score but the first goal changed the game.
“We are in one process and we need to be strong in our way. The idea at the start (of the season) was to get more competitive as a team, get closer to the other teams, and we did that.
“It is not enough yet, but next season we have to continue in our mind.”