Aubameyang links up with former Dortmund team mate Henrikh Mkhitaryan after the Armenia midfielder joined the Gunners from Manchester United last week, with Chile forward Alexis Sanchez going the other way.
Aubameyang, who scored 98 goals in 144 Bundesliga games for Dortmund, expressed his delight at the deal and his hope of emulating Arsenal's record goalscorer Thierry Henry.
"I'm happy to be here in this great team," Aubameyang told the club's website.
"I think the club have such a big history with great players like Thierry Henry, so it's an example for us strikers... he was fast and scored a lot of goals. I have to work to be like him, but I will do."
A cool finisher like former France international Henry, Aubameyang will add acceleration, power and a dose of unpredictability to Arsenal's attack.
Aubameyang is most effective as a lone centre forward but with Lacazette currently occupying that position, it remains to be seen if Arsenal manager Arsene Wenger is willing to tweak his formation to accommodate both forwards.
Should Lacazette get the nod to lead the line ahead of his new team mate, Aubameyang has shown in the past that he is capable of troubling defenders from the wings.
Aubameyang, 28, is Gabon's record goalscorer with 23 goals from 56 matches and was named the African Footballer of the Year in 2015. He was named Bundesliga player of the year in 2016 and last season was the league's top scorer with 31 goals.
"Apart from the unimpressive results of the last few weeks, we can remember that Pierre-Emerick Aubameyang's history with BVB has been a success story for more than four years," said Borussia Dortmund's sporting director Michael Zorc.
Dortmund agreed to the sale as it closed in on a loan deal for Chelsea's Belgian striker Michy Batshuayi.
(Reporting by Shrivathsa Sridhar in Bengaluru and Brian Homewood in Bern; Editing by Christian Radnedge and David Goodman)
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