As a result, expectations are predictably high, especially after Jose Mourinho explained how quickly Costa can adapt to new situations.
The Brazilian-born Spain international helped fire Atleti to an historic La Liga title win last term, breaking the duopoly of Real Madrid and Barcelona.
The Blues will be hoping he can have a similar effect on their Premier League campaign after sealing his move to England this summer, following a fruitful pre-season for the new man which included two strikes against Real Sociedad in a recent friendly win.
Paddy Power are offering new customers the chance to get a massive 9/2 (5.50) on Costa finding the net anytime against newly-promoted Burnley at Turf Moor on Monday evening. That's a significant price boost from the 6/5 (2.20) generally available on him finding the net at anytime.
Costa looks set to start the game leading the Chelsea line and should be amply supported by the likes of Eden Hazard and fellow new signing Cesc Fabregas.
Burnley are the odds on favourites for relegation this term and they are unlikely to face many stiffer tests of their Premier League credentials than the visit of Jose Mourinho's men, who now feel they have the clinical goalscorer that was missing from their squad last term.
Chelsea are just 2/5 (1.40) to bring back three points while the home side can be backed at 10/1 (11.0) to shock the title favourites and the draw is priced at 15/4 (4.80).
Burnley were only beaten twice at home in 23 Championship games last season so Clarets boss Sean Dyche will be hopeful that his side can frustrate the Blues and emerge from Monday's clash with a positive result.
After seeing Liverpool, Arsenal and Manchester City get off to winning starts over the weekend though, Mourinho will be in no doubt that his side need to hit the ground running in their first game of the campaign and the enhanced price of 9/2 (5.50) on Costa scoring at anytime is bound to prove popular with punters who believe the Spain international can make a scoring start to his Chelsea career.
|Anytime Goalscorer Enhanced Price
|New Paddy Power customers can back Diego Costa to score anytime at 9/2 with Paddy Power|
Jim Knight is Chief Betting Editor at Goal.com and has been tipping football games since he was old enough to place a bet. He is a Leicester City fan, writer and member of the We Are Going Up Podcast