It was reported earlier that a lawyer representing Kepa would be visiting La Liga head office in Madrid to make the deposit, and Bilbao's statement is confirmation that has now happened.
Kepa, who joined the Basque club at the age of nine and has been first choice since the 2016/17 season, is now expected to fly to London after already agreeing what AS reported as a 'five or six' year contract that Marca explained was negotiated with Chelsea via a third party mediator.
It is expected that 23-year-old Kepa will undergo a Chelsea medical when he arrives in London, before the transfer, a new world record for a goalkeeper, is confirmed.
Chelsea manager Maurizio Sarri is thought to want Kepa to start training with his new teammates on Thursday, with a view to selecting the Spaniard for the opening game of the 2018/19 Premier League season against Huddersfield on Saturday.
His arrival at Stamford Bridge will allow Thiabut Courtois to complete a move to Real Madrid.
The Belgian failed to report for training earlier this week in a bid to force an exit from the club, leaving Chelsea little choice but to move heaven and earth to find a replacement in the incredibly short timeframe before the imminent Premier League transfer deadline.