The teams were paired together in Friday's draw in Nyon, which also pitted Bayern Munich against Manchester United, Lyon against fellow French side Bordeaux and Inter Milan against CSKA Moscow.
Barcelona and Arsenal both recorded thumping second-leg wins in the last 16, Pep Guardiola's men beating Stuttgart 4-0 and Arsenal going one better with a 5-0 thrashing of Porto.
The Spaniards, who will play the first leg at home, came out on top when the sides met in the final four years ago, coming from behind to claim a 2-1 success.
The winners will play either Inter or CSKA in the last four.
"It's a great tie," said Barca sporting director Beguiristain.
"We are two teams who don't shut up shop and play long ball football, and this tie will be nice for the fans.
"It will be a good spectacle and we'll see if we are a little stronger than them. In any case, the best news is knowing that we will be playing the return leg at home. We are strong at home and we've shown that."
Arsenal captain Cesc Fabregas was on Barca's books as a youngster and has regularly been linked with a return to the Nou Camp, while Thierry Henry played in the 2006 final for the Gunners.
"Cesc returns to the Nou Camp but Thierry Henry will also face his former team and that makes it even more interesting," Beguiristain added.
Arsenal boss Arsene Wenger added: "I believe we will not be favourites but for me it will be a 50-50 game. That's how we have to take it.
"Of course they are a good side, so are we.
"It will be an interesting, exciting game. We have to make sure we have the belief and focus right."
There will be a second repeat of a recent final in the last eight with Bayern facing United, the team who beat them 2-1 with two last-gasp goals in the 1999 showpiece. The German side won the tournament two years later, though, beating Valencia on penalties, having beaten United in the last eight.
Both teams saw off Italian opposition in the last round, United sweeping aside AC Milan and Bayern scraping past Fiorentina.
United boss Sir Alex Ferguson is relishing the prospect of locking horns with Bayern again.
"The history of playing Bayern in past European ties tells you it's going to be a very difficult tie for us," said Ferguson.
"It'll be a fantastic atmosphere [in both games].
"They have a great stadium and good pitch and we're up against a good experienced team."
Bayern chairman Karl-Heinz Rummenigge labelled the tie a "tough but attractive draw".
"We will have to push ourselves to our limits and possibly even beyond to go through," he added on the club's website.
"Manchester are the favourites, but that is where the attraction lies: to try to beat a favourite."
The winners will be guaranteed to face French opposition in the last four with Lyon taking on Bordeaux.
Bordeaux are currently two points ahead of Lyon, the conquerors of Real Madrid, in the Ligue 1 table and won 1-0 at Lyon back in December.
Bordeaux president Jean-Louis Triaud was disappointed with a draw which guarantees a French team in the last four for the first time since 2004.
"I'm a little bit disappointed," he told Eurosport. "We talked a lot about it before, about the possibility of this.
"But we have to take what we take and we just have to get on with it and deal with it.
"It's going to be a great night and means there will be a French team in the semi-finals and that's something for French football to celebrate."
Lyon president Jean-Michel Aulas added: "It will be a very special night for us.
"We did think it could happen, we were hoping it wouldn't.
"Now we have to hope we qualify but we are going to see a French team in the semi-finals and let's hope we see one in the final."
Inter will be hot favourites to make it through against a CSKA side who have never been to this stage of the competition before.
But general director Ernesto Paolillo believes Jose Mourinho's men cannot afford to be over-confident, CSKA having won 2-1 away in Sevilla to progress.
"I believe the tie against CSKA is no easy match," he said on the club's official website.
"It would be a mistake to underestimate them for several reasons.
"CSKA have just begun their campaign and they are rested and fresh and in Moscow, you play on a synthetic pitch that favours teams that have less technical quality while the more talented teams have less control of the ball."
Bendtner scores another Hat Trick in C Lge Hat Trick: Bendtner scores another Hat Trick in Champs Lge 2010 12/1