The defending champions had drawn 0-0 with AC Milan at the San Siro in the first fixture, but triumphed 3-1 at the Camp Nou in the reverse fixture.
Two Lionel Messi penalties either side of an Antonio Nocerino strike gave the Catalans a 2-1 lead at the break, before Andres Iniesta sealed victory early in the second half.
Pep Guardiola has admitted that he is glad his side have progressed, but does not feel that the Spaniards are favourites for the tournament.
“I don’t think we are the favourites, Bayern Munich are there, Real Madrid are there,” he told Sky Sports.
“We have won two Champions Leagues in the last three years and we have reached the semi-finals five times in a row, so we have been very successful for this club.
“The most difficult thing in sport is to be consistent. You can win once or twice, but over many years to win the title is very tough.
“These players are awesome because they have shown the world the way they have to compete. We are so glad to be there and I am so happy to be their coach,” he concluded.
Meanwhile, a first-half Ivica Olic double gave Bayern a 2-0 win over Marseille at the Allianz Arena, making it 4-0 on aggregate.
Barcelona will face the winners of the Chelsea and Benfica tie, whilst Bayern will play Real Madrid or APOEL.
By Gareth McKnight