Christian Pulisic had put Chelsea forward with a smart finish in the fifth minute, but Aubameyang levelled with a penalty spot near the end of the first half before sublimely lifting in the winner with 23 minutes to go.
It means that Arsenal, who finished eighth in the Premier League, go straight into the UEFA Europa League group stage for 2020/21.
Consequently, Tottenham Hotpsurs, who ended 2019/20 in sixth position, will have to battle for a place in Europa by playing a number of qualifying games.
Wolves, who had suffered an elimination suddenly have a chance to hang on if they win the 2019/20 UEFA Europa League. If they do, there will be eight Premier League clubs in Europe in 2020/21. Wolves are currently in the Round of 16.