After being strongly linked to Real Madrid, Arrizabalaga signed a new deal with Bilbao in January that raised his release fee to €80 million from €20 million.
Chelsea have completed their third signing of the transfer window, breaking the world record transfer fee for a goalkeeper that was recently set by Liverpool when the Reds purchased Brazil worldwide Alisson Becker.
"The Spanish global goalkeeper arrives ahead of the new Premier League season, having signed a seven-year contract at Stamford Bridge", Chelsea said in a statement.
The 23-year-old would be brought in as a replacement for unsettled Thibaut Courtois.
Kepa played 30 times in La Liga for Bilbao last season and kept seven clean sheets as the Basque side finished 16th in the table.
Kepa Arrizabalaga kept a clean sheet on his Premier League debut for Chelsea
But the Foxes aren't keen to sell Maguire, especially on the cheap, so United may have to look elsewhere if they want a new face in their defence in time for Friday's Premier League opener, ironically against Leicester at Old Trafford.
Report after report has surfaced over Courtois' exit, with stories going as far to say that a fee had been agreed between Chelsea and Real Madrid for the Belgian. I just think Chelsea have made a great bet in taking me. "I find his style and ideas very attractive".
Just an hour or so after Thibaut Courtois had faced the cameras in Madrid, the world's most expensive goalkeeper Kepa was presented to the English media. The only pressure I experience is the pressure I put on myself.
"I think I will be able to adapt", he said.
"A huge thank you to all my team-mates and the technical staff, who I shared success and fantastic moments with".
"He is very happy that I am here because he knows how important it was for me to come to Real Madrid", Courtois said.More news: Paul Manafort's ex-aide Rick Gates testifies at trial on Cyprus accounts