The Dragons will face Skonto Riga, who have won their national league 11 times in succession since 1990.
"We don't know much about them," admitted manager Barry Kenny Brown, "but we've got a few weeks now to get the information we need and to prepare accordingly.
"It could have been easier for us, but we believe it's a winnable game."
The Baltic state's side have faced a Welsh team before, beating Newtown 7-1 on aggregate in 1996.
Skonto has been the starting point for many of the country's internationals, including Marian Pahars (Southampton), Igor Stepanovs (Arsenal) and Andrei Rubins (Crystal Palace) now playing in England.
The matches will be played on July 17 and July 24, and the winners will play Bulgarian side Levski Sofia.
Lucrative
Meanwhile, Bangor City have missed out on a lucrative qualifying round clash with Ipswich Town.
They were drawn in the same geographical group as the Tractor Boys but, instead of making the short trip to Suffolk, they face a clash with Yugoslavian side FK Sartid.
Sartid finished third in their national league last season behind Partizan Belgrade and Crveda Zvezda (formerly Red Star Belgrade) and defeated Dundee 5-2 in the 2001/02 Intertoto Cup.
Bangor boss Peter Davenport said he was happy to be at home in the first leg, though it will be played at Wrexham's Racecourse Ground.
"If we can get a good result at home, then you never know. We'll have to be at our best, and our players will have to be up for it.
"We will find out more about them and, hopefully, their game against Dundee will be on video so we can gain something from that."
Fellow League of Wales side TNS are also in eastern Europe, they travel to Poland for the second successive season to face Amica Wronki. Last term they were beaten over two legs by Polonia Warsaw.
Wronki, who finished third in their league, are sponsored by electrical giants Amica and have made progress into European competition in the last four seasons, going out to Athletico Madrid and Hertha Berlin in the past.
The matches will be played on August 15 and August 29.
Champions League, first qualifying round:
Tampere Utd v Pyunik
Skonto Riga v Barry Town
Portadown v FC Belshina Bobruisk
F91 Dudelange v Vardar
FBK Kaunas v Dinamo Tirana
FC Flora Talinn v Apoel Nicosia
Zeljeznicar Sarajevo v Akranes
Hibernians v Shelbourne
Torpedo Kutaisi v B36 Torshavn
FC Sheriff Tiraspol v Zhenis Astana
Uefa Cup: first qualifying round:
Group 1: Liteks Lovetch v FK Atlantas
FC Encamp v Zenit St Petersburg
FK Atyrau v Matador Puchov
Glentoran v Wisla Krakow
Group 2
FK Pobeda v FC Midtjyiland
NK Primorje v Zvartnots
FK Ventspils v Lugano
Hapoel Tel-Aviv v Partisani Tirana
Group 3
Apollon Limassol v Ferencvaros
Hajduk Split v GI Gota
SK Brann v FK Suduva
Amica Wronki v T.N.S.
Group 4
FC Copenhagen v Lokomotiv Tbilisi
FK Metalurgs v FC Karnten
FC Vaduz v Livingston
Silema Wanderers v Polonia Warsaw
Group 5
Anorthosis Famagusta v CS Grevenmacher
FC Levadia Talinn v Maccabi Tel-Aviv
Leixoes v FK Belasica
Stabaek v Linfield
Group 6
Olomouc v FK Sarajevo
Zimbru Chisinau v IFK
Ujpesti v KI Klaksvik
MyPa v Odense BK
Group 7
Dinamo Minsk v CSKA Sofia
TVMK Talinn v Dinamo Tbilisi
Servette v Spartak Yerevan
Djurgardens IF v Shamrock
Group 8
Varteks v Dundalk
Gomel v HJK Helsinki
FC Nistru Otaci v Aberdeen
IBV Vestmannaeyja v AIK Solna
Group 9
Rapid Bucuresti v HIT Gorica
Domagnano v Zizkov
Kairat Almaty v Crvena Zvezda
Metalurg Zaporizhzhya v Birkirkara
Group 10
Bangor City v FK Sartid
FK VTJ KOBA Senec v Siroki Brijeg
SK Tirana v National Bucuresti
Beggen v Ipswich
Fylkir v Excelsior Mouscron