We had two bids for Aubameyang rejected by Dortmund before agreeing a fee that eclipses the £46.5m they paid for Alexandre Lacazette in July.
Arsenal said the 28-year-old - the 2015 African Footballer of the Year - had joined on "a long-term contract".
Dortmund agreed to the sale after striking a deal to sign Chelsea forward Michy Batshuayi on loan.
Aubameyang said: "I'm really happy to be here in this great team.
"The club has such a big history and great players like Thierry Henry. He's an example for us strikers. I'm a fast player and I score goals too, like Henry a little bit. I think I have to work a lot to be like him, but I will do.
"I hope that we will come back to the top as soon as possible. I will do my best to join in."