Chelsea, who have not beaten their London rivals in any of their last 16 meetings, will be at home in the first leg.
In the semi-finals the winners of that tie will face either nine-times winners and favourites Real Madrid or AS Monaco, who play the first leg of their quarter-final in Spain.
Holders AC Milan are at home in the first leg against Deportivo Coruna, who will not be overawed by the prospect having convincingly knocked out last year's runners-up Juventus on Tuesday.
The winners will play either last year's UEFA Cup winners Porto, who eliminated Manchester United on Tuesday, or France's Olympique Lyon. They play the first leg of their quarter-final in Portugal.
With the quarter-finals missing Manchester United for the first time in eight years, Arsenal and Chelsea took up the baton for England but there was a sense of anti-climax when they were paired.
"Generally one of the joys of playing in Europe is obviously to meet overseas teams," Arsenal vice-chairman David Dein told Sky Sports News.
"To meet Chelsea, who we have already played three times this year, is a little bit anti-climactic perhaps but yet it's a massive game and it's there to be won with a very juicy semi-final if we manage to get that far."
MORIENTES THREAT
Arsenal, unbeaten in the premier league this season, have beaten Chelsea three times in domestic encounters, twice in the league and once in the FA Cup, but have yet to progress past the quarter-finals of the Champions League.
Reaching the last eight is a matter of course for Real Madrid and they will be pleased with their draw, even though they should not underestimate Monaco who thrashed Deportivo Coruna 8-3 during the group phase.
One player who might have mixed feelings about the tie is Madrid's Spanish international striker Fernando Morientes, who has spent the season on loan at Monaco.
Morientes has helped Real to three of their Champions League triumphs but Madrid director Emilio Butragueno said that the Spanish side would not try to prevent him playing in the tie.
"He played for us for many years, for him it will not be easy but he is a professional and he will try to help his team to beat Madrid," said the former Spanish international.
Five of the eight quarter-finalists -- Arsenal, AC Milan, Real Madrid, Monaco and Porto -- lead their domestic leagues. Milan and Real are the only teams in the last eight who also reached last year's Champions League quarter-finals.
The first legs of the quarter-finals will be played on 23/24 March with the returns two weeks later on April 6/7.
The semi-finals are played on April 20/21 and May 4/5 with the final in Gelsenkirchen, Germany on May 26.
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