After a goalless first half in Baku, Azerbaijan, former Arsenal striker Olivier Giroud headed the Blues in front with his 11th goal of the Europa League campaign, more than any other player, from an Emerson cross on 49 minutes.
Europa League double
The victory confirmed Chelsea's second Europa League crown, after winning the competition in 2013, and the first major trophy of Maurizio Sarri's managerial career.
Chelsea had already secured qualification for next season's Champions League, which Liverpool or Tottenham Hotspur will win on Saturday 1 June, and the Blues will face the victors of the final in the Super Cup on Wednesday 14 August.
Arsenal will compete in the Europa League again next season after finishing fifth in the 2018/19 Premier League, two places below Chelsea.