Loic Remy, Filipe Luis and Didier Drogba also moved to West London, and, although given few chances by head coach Jose Mourinho, they have done fairly well in their infrequent displays.
The performances of Costa and Fabregas have taken all the plaudits though, and have even taken the praise of a number off other impressive individuals in the Blues ranks, such as veteran Branislav Ivanovic.
The Serbian international has been his usual self in the first-team set-up for the West Londoners, with keen defensive and attacking abilities helping the Blues lead the Premier League table heading into mid-October.
Having been at the club since 2008, Ivanovic has seen a number of players arrive at Stamford Bridge, but what has pleased him most with the current batch of new stars is how quickly they have adapted to the Premier League.
Speaking to the official Chelsea Magazine, the 30-year-old full-back said: ‘It is really amazing how quickly the new players have adapted.
‘You could see straight from the first day how they work, how well they do their jobs, and that it is normal for them to play this way. That is why they are here and we are all very happy about that.’
However, Ivanovic does not feel as if they cannot improve upon their already scintillating form, with their early starts only going to get better as the first-team squad stays together.
He added: ‘As this group stays together for a long time, we will get better and better – we know each other’s games, we know the movement of each other and this gives us the opportunity to play more easily in games.
‘Sometimes we work on special things in preparation for a game, and this is one thing, but it is another to understand your team-mates, to know how they work and what they like on the pitch.
‘The moment you start to see what they usually do in training, you know they will usually do this in the game. You have to feel that.’