(CNN) -

Luis Suarez is "now a Barcelona player in all respects," according to the Spanish club.

Liverpool and the Spanish side announced last week they had agreed terms for the sale of the Uruguay international, with a transfer fee reported to be in the region of £75 million ($128.5 million.)

Suarez, who was due to sign a five-year contract with the Catalan giants, traveled to Barcelona Tuesday to complete the transfer.

Although no official announcement has been made, Barca sporting director Andoni Zubizarreta revealed in a news conference Wednesday that a deal has now been finalized.

Following the four-month ban from football-related activity imposed by FIFA on Suarez for biting Italy's Giorgio Chiellini at the World Cup, Zubizarreta conceded he had to be careful what he said about the striker.

When the transfer has been officially announced, Barcelona will be unable to unveil Suarez due to his ban.

The Spanish club have presented previous big-money signings, such as Cesc Fabregas and Neymar, to their supporters at the Camp Nou stadium.

Despite appealing, Suarez saw FIFA uphold his suspension last week, and he will now take his case to the Court of Arbitration for Sport (CAS) in Switzerland in hope that the sanction will be overturned.

Suarez joined Liverpool in January 2011 from Dutch club Ajax for £22.8 million ($39 million), scoring 82 goals in 133 appearances.

He played a pivotal role in the Reds' title challenge last year, netting 31 times in 37 appearances.

Liverpool came up just short in the race for the English Premier League title, finishing second to Manchester City, but ensured Champions League football for the first time in four seasons.

Costa signs

One long-standing transfer that has definitely been concluded is that of Diego Costa's move to Chelsea.

Costa has long been linked with a move from Atletico Madrid, and the London side announced Tuesday that a deal has been completed. It is reported that Chelsea met the striker's buy-out clause, believed to be worth £32 million ($54.8 million).

The 25-year-old, who helped Atletico to the Spanish La Liga title and the European Champions League final last season, has signed a five-year contract.

Costa, who was born in Brazil but was part of Spain's squad at the 2014 World Cup, expressed his delight at joining Chelsea, while he revealed he is looking forward to working under manager Jose Mourinho.

"I am very happy to sign for Chelsea. Everybody knows it is a big club in a very competitive league, and I am very excited to get started in England with a fantastic coach and teammates," he told Chelsea's official website.

"Having played against Chelsea last season [in the European Champions League] I know the high quality of the squad I am joining.

"I would like to thank everybody at Atletico who made me into the player I am, it was an incredible time for me, but now I am starting a new adventure and I hope to win many trophies with Chelsea."

Costa will be joined at his new club by a familiar face in former Atletico teammate Filipe Luis.

Chelsea confirmed Wednesday that an agreement has been reached to sign the left-back, who also played a key part in securing Atletico's first Spanish championship in 18 years.

Luis is reported to be joining for a fee of £20 million ($34.25 million), with the move subject to the 28-year-old agreeing personal terms with the English side.

Elsewhere, Liverpool confirmed the signing of Lazar Markovic from Benfica Tuesday.

The 20-year-old winger is the English club's fourth signing of the summer -- after Rickie Lambert, Adam Lallana and Emre Can -- and he cannot wait to get started.

"I am very happy that I have joined such a great club," he told Liverpool's official website.