The first leg of the semi-final finished 1-1 in Spain, leaving the tie in the balance, but the second leg was one-sided, with the home team dominating the game in west London.
Goals from Timo Werner and Mason Mount gave them the victory, but they had a string of chances to make the results even more comfortable than just a 3-1 aggregate win.
Edouard Mendy played well in goal for Chelsea, but Real Madrid were blunt and a shadow of the team that won three Champions League titles on the spin under Zinedine Zidane.
There may have been no fans in Stamford Bridge to see their heroes dismiss the Spanish giants, but Blues supporters will be celebrating on Wednesday night after their team booked a match against Manchester City on 29 May in Istanbul.
Drogba was one of them, tweeting: ‘Let’s goooooooooo. We are going to Istanbul my people.’
The Ivorian then referenced the fact that Chelsea’s women’s side have also reached the Champions League final, where they will take on Barcelona on 16 May.
Drogba posted a video of wild celebrations, with the caption :’When both men and women, @ChelseaFCW, @ChelseaFC are in the Champions League final.’
Real Madrid manager Zinedine Zidane was magnanimous in defeat and could only praise Chelsea, who were the superior team in both legs.
‘They deserved the win. We fought and tried but they deserved to win and go through,’ said the Frenchman.
‘The players who have played were fit to play. I’m proud of my boys: we tried, we have got this far – just one game from the final. Chelsea played a great match and have gone through and we have to say well done to them.
‘We needed to be better going forward. We didn’t have any clear chances, they made a number of them and that’s football. Now we rest and think of La Liga.’
MORE : John Terry reacts as Chelsea reach two Champions League finals and pays tribute to Mason Mount after Real Madrid semi-final win
MORE : Joe Cole and Rio Ferdinand hail Edouard Mendy for key role in Chelsea win over Real Madrid
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