Blues boss Jose Mourinho spent much of last term complaining about his lack of quality attacking options and Romelu Lukaku, Samuel Eto'o and Demba Ba have all been sent packing to make room for Costa and returning Chelsea legend Didier Drogba.

On the evidence of Costa's maiden outing in west London, the �32 million ($53 million) Mourinho splashed out to sign the 25-year-old from Atletico Madrid should prove an astute investment.

Costa was on the scoresheet with a cool finish less than a minute into his home debut and he added a second goal in the seventh minute, while proving a constant threat to the Sociedad defence before being replaced to a standing ovation on the hour.

Although Costa was the headline act, Mourinho will also have been encouraged by a solid home debut from Spain midfielder Cesc Fabregas following his move from Barcelona and a composed outing from Belgian goalkeeper Thibaut Courtois, who is tipped to push Petr Cech for his place this season.

It was a satisfying conclusion to Chelsea's pre-season preparations and the Blues will go into their Premier League opener at Burnley next Monday as a stronger unit than the one that finished without a trophy last season.

Mourinho's side were back at the Bridge for the first time since their final home fixture of last season against Norwich served as an emotional farewell for Frank Lampard and Ashley Cole -- and much has changed in those three short months.

After finishing last season empty-handed, Mourinho, under pressure to deliver silverware, has carried out an �80 million overhaul of his squad.

Most of the focus is on Costa, who fired Atletico to a surprise Spanish title last season, and he took less than 60 seconds to make a good first impression on his new supporters.

It was a perfect demonstration of the qualities Costa will bring to Chelsea as he made a clever run off the shoulder of his marker, calmly collected a Ramires pass and slotted his clinical low shot past Enaut Zubikarai from an acute angle into the far corner.

Chelsea were tearing through the Spanish side's defence every time they attacked and there were only seven minutes gone when Costa notched his fourth goal of the pre-season.

This time Andre Schurrle was granted time and space on the edge of the penalty area by Sociedad's statuesque back-line and the German World Cup winner curled a shot that struck the far post before rebounding to the unmarked Costa for a simple tap-in.

After that electric start, there was a rather more sedate feel to the rest of the half as Chelsea went through the motions against obviously inferior opposition.

Fabregas, preferred to Oscar in the playmaker's role behind lone striker Costa, caught the eye at times as he shuttled enthusiastically around midfield and dictated the tempo of Chelsea's attacks.

Mourinho made a host of changes in a low-key second half, including giving former Atletico left-back Filipe Luis his home debut.

Costa went close to completing his hat-trick when he flashed a low effort just wide from Eden Hazard's cross.

But Mourinho may want to wrap Costa in cotton wool before next week's opener because his replacement Fernando Torres, continuing the theme of his miserable time at Chelsea, squandered a chance to add a third goal when he headed wastefully over.