The German club, which last won the Champions League in 2001, missed out on a spot in European football's elite club tournament after finishing fourth in the Bundesliga last season.
Tottenham Hotspur, who reached the semi-finals of last season's Uefa Cup, will play Cypriot side Anorthosis Famagusta while Bolton take on Macedonia's Rabotnicki.
Blackburn Rovers have been drawn against Greek club Larissa, while Everton face a trip to Ukraine to play Metalist Kharkiv.
Scottish Premier League team Aberdeen are also off to Ukraine to meet one of the biggest names in European football, Dnipro Dnipropetrovsk.
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"There is no such thing as an easy draw in Europe."
Keith Wyness, Everton chief executive |
"There is no such thing as an easy draw in Europe," Keith Wyness, Everton chief executive, was quoted as saying by BBC Sport.
"Ukraine is a well-known footballing nation but Everton are very focused on taking the club further in Europe this year.
"We hope to be in Europe more consistently."
No pushover
Meanwhile, Hamit Altintop, Bayern's Turkish midfielder, believes that although his side appears to have a favourable draw their Lisbon-based opponents, who finished fifth in the Portuguese league last season, will be no pushover.
Belenenses have previously failed to get past the second round of the Uefa Cup, but are packed with creative Brazilians, and Altintop says the Germans can't afford to make any slip-ups.
"I have never heard of Belenenses or ever seen them play," said the Turkish international.
"But whether or not they are a big name doesn't matter. Often the teams without a big history are the most dangerous to play against, because they have nothing to lose.
"We will have to be on our guard."
Other big matches
Other notable clashes include Germany's Nurnberg taking on Rapid Bucharest from Romania, Switzerland's Zurich meeting Italy's Empoli, Rapid Vienna from Austria drawn against Belgium's Anderlecht and Croatia's Dinamo Zagreb in a showdown with Dutch club Ajax.
The home and away ties will be played on September 20 and October 4.
The 40 winners that progress from the first round will go into a group phase comprising eight groups of five clubs.
The top three teams of each group then progress through to the round of 32, at which point they will be joined by the eight sides that finish third in their Champions League group.
The Uefa Cup final will be held at the City of Manchester Stadium on May 14, 2008.