"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."
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.
Dortmund agreed to the sale with Chelsea's Belgian striker Michy Batshuayi heading to the Ruhr on loan for the rest of the season.
Read more: Swans glide past pop gun Arsenal
Arsenal remained the major movers as the transfer deadline loomed, selling French forward Olivier Giroud to the Blues to complete the Aubameyang merry-go- round and also retaining German playmaker Mesut Ozil until 2021 on a new deal.
"Chelsea is one of the biggest teams in the Premier League," the 31-year-old Giroud said in a statement. "They have won maybe the most trophies in the last six or seven years. It's a massive club and I am proud to sign for Chelsea, and I'm looking forward to playing."
The extension to Ozil's contract, which would take him through to 2021, is reported by the BBC to be worth £350,000 (NZ$674,000) a week before tax. That would make him the highest-paid player in Arsenal's history.
Read more: All White trains with Usain Bolt
Elsewhere, Manchester City are understood to have made another last-minute play for Leicester's Riyad Mahrez which would set another club-record fee for the Premier League leaders.
The Algeria international is understood to have been earmarked as a potential late target for Pep Guardiola's side after the blow of losing Leroy Sane to injury.
Reports on Wednesday claim that the Premier League leaders have made an improved offer believed to be around £65million (NZ$125.1m) plus an unnamed player to bring Mahrez to the Etihad.
The Foxes are believed to have agreed a loan deal to send striker Islam Slimani to Newcastle, while Davy Klaassen's proposed move from Everton to Napoli is off after talks broke down.
Watford winger Isaac Success agreed to join Spanish side Malaga on a loan deal until the end of the season.
To get the day's top sports stories in your inbox, sign up to our newsletter here