Arsenal will play Udinese in the Champions League play-off round, and four-time winners Bayern Munich were drawn against FC Zurich yesterday.
Lyon received perhaps the toughest draw, against a match-sharp Rubin Kazan who are midway through the Russian league season.
Arsenal club secretary David Miles said the Gunners were happy to avoid the long trip to Russia.
"It would have been difficult. But we won't underestimate Udinese at all. The draw gives us the home leg first and hopefully we will take a lead over there," Miles said.
Villarreal will travel to Denmark for the first leg against Champions League newcomers Odense. Twente will host two-time winners Benfica in the first leg.
In a separate 10-team draw for national champions, Copenhagen were drawn against Czech newcomers Viktoria Plzen.
First-leg matches are played on 16 and 17 August, and the returns on 23 and 24 August.
Ten play-off winners will join 22 teams with direct entry to the lucrative group stage, which is drawn on 25 August in Monaco.
Arsenal, the 2006 Champions League runners-up, and Udinese have never met in a competitive match.
The English side has a slight edge with the Premier League scheduled to begin next weekend, whereas Udinese's Serie A campaign starts on 28 August.
"We will make our best effort to prepare our team in the best way," Udinese general manager Franco Collavini said. "We respect Arsenal. It's one of the most important clubs in Europe."
Udinese, who were not seeded in the draw, qualified for the Champions League by finishing fourth in Serie A. The club then sold star winger Alexis Sanchez to Barcelona and key midfielder Gokhan Inler to Napoli.
"We are working to complete our squad by August 31. We're not running to complete our squad for the Champions League play-offs," Collavini said.
Bayern Munich received a favourable pairing with Zurich, who lost their first three matches in the Swiss league this season before eliminating Belgium's Standard Liege in the third qualifying round.
"We have good chances of reaching the group stage," Bayern coach Jupp Heynckes said.
Still, he cautioned that "Swiss football has great value" and noted that Zurich finished only just behind FC Basel last season, saying "that speaks for the quality of the club."
"We will watch the team closely at the weekend," Heynckes said.
Twente will find out next week if they can host Benfica in their Grolsch Veste stadium where two men died in a July construction accident as a new stadium roof collapsed.
"We are involved with the families of the two young boys who tragically died," Twente technical manager Cees Lok said. "It was a big traumatic event but slowly the focus went back to football."
Twente played 90 kilometres away in Arnhem when they won 2-0 in the home leg of a third qualifying round tie against Romania's Vaslui.
"We're hoping to play in the home stadium against Benfica," Lok said. "Every team we play against, we are the underdogs. But I think we are a tough opponent."
In other pairings of national champions, Wisla Krakow play APOEL, Maccabi Haifa face Genk, Dinamo Zagreb play 1979 runners-up Malmo and BATE Borisov face Sturm Graz.
Play-off Round
League Route
Odense (Denmark) vs. Villarreal (Spain)
Twente (Netherlands) vs. Benfica (Portugal)
Arsenal (England) vs. Udinese (Italy)
Bayern Munich (Germany) vs. FC Zurich (Switzerland)
Lyon (France) vs. Rubin Kazan (Russia)
Champions Route
Wisla Krakow (Poland) vs. APOEL (Cyprus)
Maccabi Haifa (Israel) vs. Genk (Belgium)
Dinamo Zagreb (Croatia) vs. Malmo (Sweden)
FC Copenhagen (Denmark) vs. Viktoria Plzen (Czech Republic)
BATE Borisov (Belarus) vs. Sturm Graz (Austria)