The Gunners booked their place in the last eight with a comfortable 9-3 aggregate win over PSV after thumping the Dutch side 7-1 in the first leg.
Villa reached the quarter-final of Europe's elite club competition for the first time in 42 years following a stunning 3-0 win over 10-man Club Brugge to go through 6-1 on aggregate at Villa Park.
The Villans previously competed in the European Cup and have become the first team since Atalanta in 2019/20 to reach the last eight of the Champions League in their debut season.
They will face in-form PSG who progressed after beating Liverpool on penalties at Anfield on Tuesday.
It will mean a return to the Parc des Princes for on-loan PSG striker Marco Asensio who scored twice for Villa against Club Brugge after coming on as a second-half substitute.
Defending champions Real Madrid are through to the quarter-finals after a nervy penalty shootout win over city rivals Atletico after their match ended 2-2 on aggregate.
Arsenal will play the first leg at Emirates Stadium before travelling to the Santiago Bernabeu, while Aston Villa face PSG at the Parc des Princes and host the return leg at Villa Park.
The quarter-finals will be held on April 8/9th and 15/16th.
Champions League quarter-finals
First leg
Arsenal v Real Madrid - April 8th
PSG v Aston Villa - April 9th
Barcelona v Dortmund - April 9th
Bayern v Inter - April 8th
Second leg
Real Madrid v Arsenal - April 16th
Aston Villa v PSG - April 15th
Dortmund v Barcelona - April 15th
Inter v Bayern - April 16th