The Irish Premiership champions are away to the Bulgarians, who have won their domestic title for the last seven seasons, in the first leg.
The first leg will be played on Wednesday 11 July, with the return game at Seaview on Tuesday 17 July.
The game in Bulgaria will have an 18:00 BST kick-off, with the return leg starting at 20:00 BST.
Cork City of the League of Ireland Premier Division will play Poland’s Legia Warsaw after Tuesday’s draw.
“Ludogorets have got a great pedigree in the Champions League,” said Crues captain Colin Coates.
“They drew at home to Liverpool a few years ago and only narrowly lost to them at Anfield, so that tells you about what level they are at.
“But I’m sure Stephen (Baxter) will work out a game plan for us over the next few weeks.
“Our biggest challenge will be securing a result away from home as it will be tough to keep our shape and discipline, especially in the heat.
“Apart from FC Copenhagen, we have proved in recent years in Europe that we can give anyone a match at Seaview, including Fulham and Rosenberg.”