The BBC will broadcast both United's games against the winners of the previous round's qualifying tie between Hungarian team Zalaegerszegi and Croatian outfit NK Zagreb.
The opening leg of the tie, where United will visit either Hungary or Croatia, takes place on 14 August with the return match on 27 August.
United's presence in the preliminary stages is the first time the team has failed to qualify outright for the Champions League and came about due to the club's relatively lowly finish of third in the English Premiership.
The BBC's move to secure the rights is also the first time it has screened Champions League coverage with terrestrial rival ITV holding the rights to all the games during the main stages of the competition.
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