Gabon striker Aubameyang, 33, scored 13 goals in 24 appearances for Barca after joining the Spanish club in February from Arsenal.
Left-back Marcos Alonso has left Chelsea by mutual consent and is expected to sign for Barcelona.
Chelsea have the option to sign Zakaria on a permanent deal.
The 25-year-old Switzerland international only joined Juve from Borussia Monchengladbach in January.
When Aubameyang signed for Barca he had a buyout clause of 100m euros (£83.4m) in his contract, but has only played eight minutes this season. Barcelona have been looking to offload players after spending almost £200m on new arrivals despite being more than £1bn in debt.
The deal for Aubameyang means Chelsea chairman Todd Boehly has spent around £270m in his first transfer window since buying the club from Roman Abramovich – the highest amount any English club has spent in a single 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.’
Aubameyang scored 92 goals in 163 games in all competitions for Arsenal, but left on a free transfer after falling out with manager Mikel Arteta.
That departure played a big part in the Gunners documentary All or Nothing.
Only four players have scored more Premier League goals than Aubameyang’s total of 68 in the period since 31 January 2018 – the date he joined Arsenal.
Aubameyang worked with Chelsea boss Thomas Tuchel at Borussia Dortmund between 2015 and 2017.
He scored 79 goals in 95 games under the German, 38 more than he netted under any other manager.
This summer the Blues have also brought in nine players including Leicester’s French defender Wesley Fofana for a fee in the region of £70m, England forward Raheem Sterling from Manchester City for £50m, Senegal defender Kalidou Koulibaly from Napoli for £34m, English midfielder Carney Chukwuemeka from Aston Villa for £20m, Spain left-back Marc Cucurella from Brighton for £62m.
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.’
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