The IFA Premiership winners will be looking to take full advantage of the first leg played at Windsor Park in Belfast on July 12/13 against the only Belarusian team to have qualified for the group stage of the Champions League, in 2008-09.
League of Ireland Premier Division winners Shamrock Rovers were paired with Estonian side FC Flora Tallinn.
The Hoops - who were beaten by Italian giants Juventus in last season's Europa League qualifiers - are also set to be at home for the first leg, ahead of their away trip on July 19/20.
HJK Helsinki will provide the opposition for Wales Premier League champions Bangor City, who will travel to Finland for the first leg.
Should any of the three sides make it through to the third qualifying round, there is the chance they could face Scottish giants Rangers.