With places in the group stage of the tournament up for grabs, the stakes will be high on Wednesday and Thursday as 64 sides do battle in crucial first leg ties.
Stjarnan could not have hoped for a higher-profile draw after negotiating a way past Bangor City, Motherwell and Lech Poznan to the competition's play-offs.
Stjarnan top the table in Iceland's Urvalsdeild by three points and striker Veigar Pall Gunnarsson cannot wait to pit his skills against the 18-time Italian champions on Wednesday.
"To play with Stjarnan, my boyhood club, against a team [like Inter] is a dream come true. We have to believe there is always a chance," he is quoted as saying on UEFA's official website.
Inter, who did not play European football for the first time since the 1999-2000 campaign last term, could give competitive debuts to the likes of Nemanja Vidic, Pablo Daniel Osvaldo and Yann M'Vila.
No club has won Europe's second-tier club competition more than Inter. They have won it three times, in 1991, 1994 and 1998, while they were also runners-up in 1997.
Villarreal, who finished sixth in La Liga last season, begin their tie in Kazakhstan as they meet Astana, while Tottenham – fresh off a last-gasp 1-0 Premier League win at West Ham United on Saturday – go to Cyprus for a clash with AEL.
Tottenham have won the competition twice, in 1972 and 1984, the club's Premier League counterparts, Hull City, start with a tricky trip to Lokeren.
Another two-time winner, Feyenoord, are unbeaten in two Eredivisie matches so far in 2014-15 and will hope to continue that run when they face Zorya of Ukraine.
Fellow Dutch side PSV have started the new campaign even better, with two wins helping them to the top of the league. PSV host Belarusian outfit Shakhtyor on Thursday.
Real Sociedad - who reached the group stages of the Champions League last term – host Russian outfit Krasnodar, while Borussia Monchengladbach, two-time winners of the competition, travel to Bosnia to play Sarajevo in their first leg.
Two wins from as many games has Saint-Etienne sitting second in Ligue 1 and they will be full of confidence ahead of their trip to Karabukspor.
Fellow French side Lyon begin with a home clash against Astra of Romania.
Sparta Prague are in action against PEC Zwolle of the Eredivisie, while Panathinaikos host Midtjylland, Young Boys meet Debrecen and Qarabag do battle with Twente.
Four Croatian sides are also in action, as Hajduk Split and Dinamo Zagreb visit Dnipro Dnipropetrovsk and Petrolul Ploiesti respectively, while Split host Torino and Rijeka welcome the visit of Sheriff.
There are also four Russian teams involved, with Krasnodar joined by Lokomotiv Moscow and Rostov – who have away ties against Apollon and Trabzonspor, respectively – and Dinamo Moscow.
Dinamo play host to Omonia Nicosia in their first leg.
Legia Warsaw travel to Aktobe while another Polish side, Ruch Chorzow, battle Metalist.
Other ties see HJK face off against Rapid Wien, while Dinamo Minsk, Elfsborg and Zimbru are at home to Nacional, Rio Ave and PAOK respectively.
Zurich hit the road to tackle Spartak Trnava and Partizan clash with Neftci, and there are home ties for Asteras Tripolis, who meet Maccabi Tel Aviv, and Grasshopper, who play Club Brugge.
