The Blues were in a reasonably strong position heading into the second leg of their semi-final clash after a 1-1 draw in the Spanish capital last week.
Chelsea FC broke the deadlock before the break when Timo Werner nodded a header into the net after excellent play from N’Golo Kante.
The west London outfit wasted a couple of chances to extend their lead before Mason Mount finally secured their place in their third Champions League final by scoring with five minutes left to play.
Fabregas won the Premier League title with Chelsea FC but the Spain international didn’t feature in a Champions League showpiece during his stint at Stamford Bridge.
But the former FC Barcelona midfielder was quick to take to Twitter to congratulate Chelsea FC on their 2-0 win over Real Madrid and their place in the Istanbul showdown.
Mount was the second youngest Englishman to score in a Champions League final behind former Manchester United striker Wayne Rooney.
Chelsea FC won their only European Cup in 2012 when Didier Drogba scored the winning spot-kick against Bayern Munich in the penalty shootout in Munich.
The Blues lost to bitter rivals Manchester United in the Champions League final in 2008.