The move bolsters Arsene Wenger's attack and reunite the Gabon international with former Dortmund teammate Henrikh Mkhitaryan.
The deal was announced after drawn-out negotiations with Dortmund over the transfer fee.
Aubameyang is Arsenal's second major signing of the January transfer window after Mkhitaryan joined from Manchester United in a swap deal for Alexis Sanchez.
The duo formed a partnership at Dortmund before Mkhitaryan's move to Man United in 2016, and Wenger is hoping their combined talents will be more than enough to offset Sanchez's departure.
Aubameyang is reportedly getting a deal worth £180,000 a week, making him the highest paid player in Arsenal history -- although Mesut Ozil would be expected to eclipse that figure if he signs a new contract.
The 28-year-old arrives with high expectations, having scored 79 goals in all competitions over the last two seasons. He will become part of a formidable front four together with Mkhitaryan, Ozil and Alexandre Lacazette -- although it remains to be seen how Wenger manages to fit all that attacking talent into the same line-up.
While Arsenal could still make a late bid for West Brom defender Jonny Evans, the capture of Aubameyang represents the highlight of what has been the most active January transfer window of Arsene Wenger's 21-year reign.
Aside from Sanchez, Arsenal have also sold Theo Walcott and Francis Coquelin in a major shake-up of the squad. Arsenal have struggled badly during the first half of the season, falling to sixth place in the Premier League and losing in the third round of the FA Cup for the first time under Wenger.