Aubameyang, 28, has been subject of negotiations between the Gunners and Dortmund for several weeks, with Arsenal having refused to meet the Bundesliga side's €70m asking price.
Goal understands the Gabon international has already agreed personal terms with the north Londoners, with an official announcement to arrive in the coming days.
The striker, who scored 31 league goals last season, was left out of two consecutive games for Dortmund after missing a team meeting, with head coach Peter Stoger accusing the frontman of not being focused.
"We are ready to agree a transfer under certain parameters, but only if these are fully met," sporting director Michael Zorc told German TV.
"We have a clear position. Arsenal has made several attempts so far. We have refused them all up to now."
Aubameyang would join up with former Dortmund team-mate Henrikh Mkhitaryan at Arsenal after the Armenian joined in a swap deal which saw Alexis Sanchez head to Manchester United. The duo combined for 62 goals in all competitions two seasons ago.
This season, Aubameyang has scored 21 goals in 24 matches in all competitions. He has found the net 141 times since joining BVB from Saint-Etienne for €13m in July 2013, and he also has 23 goals in 56 caps for Gabon.
The 28-year-old's on the verge of joining an Arsenal side that sit sixth in the Premier League table, five points off the pace in the race for the top four.
The Gunners were eliminated in their FA Cup third round meeting with Nottingham Forest earlier this month but have advanced to the Carabao Cup final against Manchester City and will face Swedish side Ostersunds in the Europa League last 32.
As previously reported, West Brom defender Jonny Evans is also a target at the Emirates Stadium, although a hamstring injury sustained at the weekend could see a transfer put on hold until the summer.
Evans is open to a move, but Arsenal may face a late battle, with the likes of Liverpool and Manchester City also keen to land the former Manchester United player, depending on his fitness status.