The young Gers will take on the Slovakian side at Firhill on Wednesday night before making the trip to Bratislava for the second-leg in three weeks time.
Rangers booked their place in the second round on away goals following a 5-5 aggregate draw with Young Boys, while Slovan Bratislava made it through on penalties against Ludogorets.
It is the first time the club have competed in the UEFA Youth League, gaining qualification by winning the Under-18’s league last season.
Over 900 Gers fans turned out to support the Under-19’s last month against Young Boys, and head coach Graeme Murty is hoping for more of the same on Wednesday night.
He said: “What we need to make sure is that we bring energy and we bring the tempo and we push the issue at home because we really enjoyed the first game at Firhill.
“If we do that and we play to our utmost potential I think we can have a positive evening.
“We also need to make sure that we realise it is only going to be half-time at the end of the game, we need to make sure that we put ourselves in a positive situation going away over to Bratislava.
“We need these guys to experience a crowd, we need them to take that emotional and psychological step of playing with pressure and playing in front of a crowd and it would be fantastic if it was on Wednesday.”
Kick-off is 7pm on Wednesday night and fans can pay at the gate. Admission is £5 for adults and £3 for children.