* I have unfinished business in England, says Spaniard
* Chelsea pay fee of 33 million euros - media reports (Adds Xavi quotes)
By Clare Lovell
LONDON, June 12 (Reuters) - Chelsea will be hoping Cesc Fabregas can boost their firepower after the Barcelona midfielder agreed to sign a five-year deal with the Stamford Bridge club on Thursday.
Fabregas, 27, in Brazil with Spain's World Cup squad, will return to London after leaving Arsenal to rejoin his boyhood club in 2011.
Spanish media reported Chelsea had paid 33 million euros ($44.6 million) for the 2010 World Cup winner, with a possible three million more linked to performance.
Switching allegiance from north to south west London, he joins Jose Mourinho's Chelsea side that finished third in the Premier League and reached the semi-finals of the Champions League last season despite having trouble scoring goals.
Fabregas is likely to team up with prolific Atletico Madrid striker Diego Costa, a much publicised transfer target for Mourinho, at Stamford Bridge next season.
"I do feel I have unfinished business in the Premier League and now is the right time for my return," Fabregas told Barcelona's website (fcbarcelona.com).
"Everyone knows Arsenal had the first option to sign me. They decided not to take this option and therefore it wasn't meant to be.
"I considered all the other offers very carefully and I firmly believe Chelsea is the best choice. They match my footballing ambitions with their hunger and desire to win trophies."
Fabregas, who played for Barcelona as a child before joining Arsenal at the age of 16, made 151 appearances under three coaches, scoring 42 times for the Catalans but, unlike his time in north London, never proved a favourite among the fans.
The Spaniard's goalscoring flair will come in handy at Chelsea where compatriot Fernando Torres and his fellow strikers Samuel Eto'o and Demba Ba managed fewer than 20 league goals between them last season.
Chelsea are also losing the club's all-time top scorer Frank Lampard who often scored 20 goals a season in all competitions during his 13 years at the club.
Fabregas is moving into a crowded area of the team because Chelsea have a wealth of young, attacking midfield talent in Belgium's Eden Hazard, Brazilian duo Oscar and Willian, Germany's Andre Schuerrle and Egyptian Mohamed Salah.
The Spaniard became the youngest player to turn out for Arsenal when he made his debut in 2003 at the age of 16.
Fabregas won the FA Cup with the club but other trophies eluded the Gunners and the Catalan is clearly chasing sliverware.
During his three years at Barcelona he won the league and the Spanish Cup but their superiority could be on the wane after they were eclipsed by Champions League winners Real Madrid last season and the rising force of La Liga winners Atletico Madrid.
While Fabregas has an impressive string of international honours to his name with World Cup and European Championship medals, he has, as yet, missed out on Premier League and Champions League glory.
He clearly hopes to remedy that under Mourinho who has won both trophies twice.
Fabregas joins an expanding band of Spaniards at Chelsea where Torres has said he plans to stay, Cesar Azpilicueta is settled in defence and Brazil-born Diego Costa looks likely to be leading the line when the new season opens in August.
The midfielder has been given the number four shirt vacated by Paris St Germain-bound David Luiz.
Xavi, Fabregas's 2014 World Cup colleague and former Barca team mate, said the transfer was "great news for Cesc".
"I see him looking very happy," Xavi told reporters in Salvador. "It's a great opportunity for him to be signed by a good team.
"He was hopeful it would happen. He now knows what his future holds for the next few years but of course it is a very important loss for Barcelona." (Editing by Martyn Herman and Tony Jimenez)