Brazil central defender Alex completed his move from PSV Eindhoven to Chelsea on Friday.
"Alex Rodrigo Dias da Costa today passed a medical and signed a three-year contract with Chelsea," said a brief statement on the London club's Web site (www.chelseafc.co.uk).
Completion of the 25-year-old's move had been delayed for more than a week due to the Premier League team's application for a work permit.
Alex, who began his career at Santos, helped PSV win three successive Dutch league titles.
He played in the Brazil side that won the Copa America with victory over Argentina in the final in Venezuela on July 15.
