Manchester City boss Pep Guardiola says guiding the club to a first Champions League final "now makes sense" of his five-year spell in charge at Etihad Stadium.
Riyad Mahrez's second-leg double against Paris St-Germain secured a 2-0 win and sealed a 4-1 aggregate victory.
The Blues are one win away from a third league title under Guardiola but he had failed to steer them past the quarter-finals in Europe until this season.
"This is remarkable," said Guardiola.
"People believe it's easy to arrive in the final of the Champions League. Getting to the final now makes sense of what we have done in the past four or five years.
"Every day these guys have been consistent. We scored a goal through the hips [of the defensive wall] in the first game, and today Marquinhos hit the bar in the first half - you can be out for little details.
"Manchester United won a title because of John Terry's slip and scored in the last minute against Bayern Munich and Real Madrid won a title against Atletico in the 93rd minute. It's a competition that is so difficult and something in the stars is involved in that.
"I want to thank the owner, the chairman and the staff at the club. This club is about all the people that work behind the scenes, it's not just about money. If you want to think that then you are wrong."
Guardiola's side have been knocked out in the quarter-finals in the past three seasons by Lyon, Tottenham and Liverpool and lost in the last 16 to Monaco in his first campaign in charge.
They are playing in the Champions League for a 10th successive season and had only once before reached the semi-final stage, losing 1-0 over the two legs to Real Madrid in 2015-16 when they were managed by Manuel Pellegrini.
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'When the difficult times come, we step up'
City fell behind in the first leg in Paris when Marquinhos headed home a corner, but fought back in the second half to earn a 2-1 advantage.
Mahrez, who scored the winning goal in Paris, was again the star in Manchester, slotting under Keylar Navas in the 11th minute, before rounding off a scintillating counter-attack just after the hour mark.
Just like in the first leg when former Everton midfielder Idrissa Gueye was sent off, Mauricio Pochettino's PSG side were reduced to 10 men after Angel di Maria stood on City midfielder Fernandinho after the ball went out of play.
"We could have scored more," Mahrez told BT Sport. "They lost their nerve and started to kick us and after the red card it was more comfortable.
"We didn't concede much and I think that's why we're in the final."
Kyle Walker, who was part of a back four that kept their eighth clean sheet in this season's competition, said he was "buzzing" and "it is what you dream about".
"In big occasions there are going to be nerves - we have to control that," the right-back said.
"We go back to Anfield [in 2018] and throwing it away in the first leg. The second year we are at Tottenham  and lost in the first leg before chasing it here. Last year [against Lyon] it was different over one leg - a proper cup game.
"To finally get the victory over there and then come here and win is full credit to this squad."
Ruben Dias, who joined the Blues from Benfica in the summer, said the two legs showed the "real character of the team".
"When we went in to half-time in Paris losing 1-0 and we put on a show - that says the most about our team," the Portugal international told CBS Sport.
"When the difficult times come, we step up."
'This win propels them to the stage they want to be'
Since Manchester City were taken over by Sheikh Mansour in 2008 they have won four Premier League titles, two FA Cups and six League Cups but Europe has been a different proposition.
Guardiola was brought to the club to change that, having won two Champions League titles while in charge of Barcelona, and former City defender Joleon Lescott said the club reaching their first final had been a "long time coming".
"To see where they've come from to now go into this competition as favourites, it's special and all the fans feel the same way," Lescott said on BT Sport.
"It's been great to watch but it's been a long time coming and a lot of hard work. This win propels them to the stage they want to be at."
Former goalkeeper Joe Hart was also part of the BT Sport team and he said it was a "huge moment" for the club.
"People say this club has not got history at European level and it hasn't, but it has a real soul - people have been through the highs and lows," Hart said.
Nedum Onouha, who played for City between 2004 and 2012, told BBC Radio 5 Live it was "very surreal".
"I was at Wembley in 1999 watching that Division Two play-off final and now I'm watching the team which I support literally control the Champions League semi-final against a side who was in the final the year before," he said.
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