Manchester United will also notably play at home to 2022 Europa League runners-up Rangers and go to Portugal to play Porto, another of Jose Mourinho's old sides.
Sporting Lisbon will face Porto in the Portuguese Cup final on May 26, aiming to secure a double.
David Raya, on loan from Brentford, said it was a "great moment personally and collectively".
Arsenal last made it to the Champions League quarter-finals in 2010, when they beat Porto in the last 16, but it is the Portuguese club who now have the upper hand.
Mikel Arteta said the dream of Arsenal winning the club's first ever Champions League at Wembley is in his players' minds as they make a long-awaited return to the knockout stages at Porto.
PSG drew 1-1 away to Group F winners Borussia Dortmund to go through as runners-up after AC Milan came from behind to beat Newcastle at St James' Park and eliminate Eddie Howe's side.
Holders Manchester City and RB Leipzig became the first teams to reach the last 16 of this season's Champions League on Tuesday.
Barcelona have been eliminated in the opening stage in the past two editions but this hard-fought triumph on the road puts them in a strong position as Group H leaders to avoid a third consecutive strike-out.
For the first time since 2006, both Inter and AC Milan have reached the quarter-finals of the Champions League.
Romelu Lukaku boosted Inter Milan's chances of reaching the Champions League quarter finals for the first time in over a decade after scoring the only goal in Wednesday's 1-0 win over Porto
Porto sealed top spot in Champions League Group B with a 2-1 win over Atletico Madrid on Tuesday
Arsenal completed the signing of highly-rated Porto midfielder Fabio Vieira in a 40-million-euro deal on Tuesday.
Portuguese midfield star Fabio Vieira is to join Premier League side Arsenal from Porto for 35 million euros
Liverpool Football Club has completed the signing of Luis Diaz from FC Porto, the Premier League club announced on Sunday.
Lionel Messi opened his PSG account as the French side beat Man City while new boys Sheriff Tiraspol shocked Real Madrid in the Champions League.
Chelsea vs Porto: Chelsea reached the Champions League semi-finals for the first time since 2014 despite a 1-0 defeat against Porto in Tuesday's quarter-final second leg.
Chelsea and FC Porto meet in the second leg of Champions League quarter final on Wednesday.
Mason Mount became Chelsea's youngest ever scorer in the Champions League while Ben Chilwell's goal meant the club boasted two English scorers in a UCL game for the first time since 2012.