The English Premier League side drew 0-0 at home with Ukraine's Dynamo Kiev to reach the last eight with a 3-1 aggregate win.
The progress represents a huge achievement for outgoing coach Manuel Pellegrini, who will be replaced by Pep Guardiola at the end of the season, since City were a club adrift in Europe when he took charge in 2013.
In the two previous seasons, City -- English champions in 2012 -- had never managed to get out of their Champions League group.
But that all changed when Pellegrini replaced Roberto Mancini as coach and in both the Chilean's first two seasons, he took City into the Last 16.
Both clashes came against Barcelona, which resulted in early exits for the men in blue, but City's fortunes changed when they finally won a group for the first time, as they did last December when topping Group D.
This time, they were paired against less strong opposition in Dynamo Kiev, who may be leading the Ukrainian league with 16 wins out of 18 but who represent a very different challenge.
City made light of the first leg, winning 3-1 in the Ukrainian capital, but could only muster a tepid goalless draw on Wednesday night.
Nonetheless, scenes of joy erupted at the final whistle -- with huge smiles on the faces of the City players -- as the club finally broke new ground.
"We are really satisfied. We made history," said defender Pablo Zabaleta later. "We have been really working hard for this moment -- to make this club even bigger."
"The Champions League, we are trying to reach the final. It's really hard, but today it was job done."
City owner Sheikh Mansour now has some reward to look back on in Europe, where the billion dollars he has spent since taking charge in 2008 has previously failed to make much impact (albeit while delivering five domestic trophies, including two Premier League titles).
Meanwhile, Pellegrini has led a team into the quarterfinals for the fourth time, following previous visits with Spanish clubs Villareal (2005/6, 2008/9) and Malaga (2012/13).
He will now hope to go one better than his 2006 run, when he took Villareal to the semifinals.
Even though City will be in Friday's quarterfinal draw for the first time, and buoyed by the potential return of Kevin de Bruyne ahead of next month's matches, the win came at a cost.
Vincent Kompany limped off after just six minutes, with the captain facing another spell on the sidelines in an injury-ravaged season.
Fellow center back Nicolas Otomendi also went off with injury, so leaving Pellegrini with a defensive headache ahead of the Manchester derby on Sunday.
Dynamo failed to win in England at the 14th attempt but they did at least avoid defeat for only the third time.
Elsewhere, Atletico Madrid of Spain and Dutch side PSV Eindhoven, in the knockout phase for the first time in nine years, needed a penalty shootout to separate the sides.
This was after both legs and extra-time failed to produce a goal.
Runners-up in 2014, Atletico clinched the shootout 8-7 as veteran Juanfran slotted home the decisive kick after an engaging match in the Spanish capital.
He revealed later that it was the first penalty he had taken for the club he joined five years ago.
On Wednesday, Bayern meet Juventus while Barcelona host Arsenal for the right to take the two final quarterfinal places on offer.