Everton will take on Czech side Sigma Olomouc in the Europa League play-offs.
The Toffees, who reached the FA Cup final last season and finished fifth in the Barclays Premier League, will be at home in the first leg against the side who knocked out Aberdeen in the third qualifying round of the competition.
Hearts will face Croatian side Dinamo Zagreb, who were eliminated from the Champions League after a 3-2 aggregate defeat to Red Bull Salzburg in the third qualifying round.
Fulham's reward for beating Vetra of Lithuania 6-0 on aggregate in the third qualifying round is a tie against Russian Premier Liga side Amkar Perm.
Amkar finished fourth in their domestic league to qualify for the competition but are only 12th in the 2009 campaign with four wins from their 16 games.
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