Aubameyang only left the Emirates Stadium for Barcelona in February after his contract was terminated following several disciplinary issues and a falling-out with manager Mikel Arteta.
He scored 11 goals in 17 LaLiga appearances for Barca but, with their financial issues meaning they needed to ship players out, he was available should another club come in for him.
Arsenal's London rivals Chelsea were that club and the 33-year-old Gabon forward has been reunited with Blues boss Thomas Tuchel, his manager at Borussia Dortmund.
Aubameyang has agreed a two-year contract at Stamford Bridge to become the Blues' sixth senior signing of the transfer window.
Aubameyang said: 'I'm really happy. It's an honour to be part of this team and I can't wait to start. I have some unfinished business with the Premier League so it's good to be back and really exciting."
Chelsea chairman Todd Boehly said: "Pierre-Emerick is an elite striker with a proven track record in the Premier League and his arrival strengthens our squad, giving us new attacking options.
"We are thrilled to have Pierre-Emerick on board with us in the new era at Chelsea and we're really looking forward to working with him."