The London club, who last played in Europe in the 2006-07 season, are scheduled to visit Lusitans' 1,000-capacity Camp d’Esports d’Aixoval on July 2 in the first qualifying round tie with the return one week later.
However, the matches could be reversed to avoid a fixture clash as Andorra’s other representatives Sant Julia were also drawn at home to Denmark’s Randers in the first leg.
England were awarded an extra place in the competition after topping the fair play rankings of organisers UEFA and West Ham took it after finishing first in the Premier League's fair play list.
One hundred and two teams went into the hat for Monday’s draw, made only two weeks after the end of the European season.
Those sides included former European champions Red Star Belgrade who were drawn against Kazakhstan's Kairat Almaty and face a marathon journey to Central Asia for the second leg.
(Writing by Brian Homewood, editing by Tony Jimenez)
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