It is the first time Juventus have reached the quarter-finals since they were demoted to Serie B in the 2006 match-fixing scandal.
"Celtic is a great squad, we were very focused, very prepared. We knew that this is a team that if you don't study well, can hurt you," Juventus coach Antonio Conte said.
"To have managed to return to the top eight of football after so many years fills us - staff, players and whole club - with pride and enthusiasm."
Juventus can start thinking about a possible Champions League and Serie A double, as they lead the Italian league by six points.
"Now we're in the really intense part of the season, where you can't afford to make a mistake," Conte added.
"We have to be very good, very focused in training as well as in the matches. We know we can get a lot of happiness out of this season, but it will be very difficult."
Juventus extended their unbeaten streak in Europe to 18 matches, having lost just one in their last 30 - including qualifying. The Italian club have not conceded a goal in their last five.
As in the first leg, Celtic created plenty of chances but failed to take advantage, while the Italians were ruthlessly efficient at the other end.
"The difference is quality in the final third," Celtic coach Neil Lennon said. "We had good chances again tonight and we didn't take them. We played really good football and we missed really good chances to get back into the game. Quality is the real difference, quality counts and that was what made the difference over the two games."
It is the end of an impressive European campaign for Celtic, who memorably beat Barcelona in the group stages as well as winning away at Spartak Moscow.
"These young players have achieved so much this campaign," Lennon added.
"I hope they learn from it but we won't know until we come into the competition again.
"It's going to be very difficult to keep these players. Some want to progress their careers maybe outside Scotland and we understand that. We've just come off the back of an unbelievable experience in the Champions League. The handicap we have is we're £100 million [$184 million] behind the other teams in the league."
With the tie all but decided already, Juventus rested midfielders Stephan Lichtsteiner and Claudio Marchisio, who were both one booking away from a suspension.
In yesterday's other match, Paris Saint-Germain drew with Valencia to qualify for the last eight 3-2 on aggregate.
Juventus 2
Celtic 0
Paris St-Germain 1
Valencia 1
- AP
