The 23-year-old is expected to replace Thibaut Courtois at Stamford Bridge for a record fee that would surpass the 72.5 million euros Liverpool paid Roma for Brazilian Alisson last month.
"At 12:02 p.m. (1002 GMT) on Wednesday, August 8, La Liga informed our club that the player, Kepa Arrizabalaga, had met the conditions to unilaterally break his contract that linked him to Athletic Club," the Spanish side said in a statement.
"The amount of the compensation established in the contract has been deposited.
"Athletic thanks the player for his contribution during the time he has remained in our club."
In Spain, instead of the buying club paying the selling club the amount set by the contract, the player must buy himself out.
This is done by depositing the amount of the buyout clause with La Liga to release the player. La Liga then pass the money onto the selling club.
Chelsea's move for Kepa comes with Belgium number one Courtois strongly linked with Real Madrid, having yet to report to training with the Premier League club following the World Cup.
Kepa has played 53 times in La Liga for Bilbao over the last two seasons, and made his international debut in a 5-0 friendly win over Costa Rica in November 2017.
He was also in the Spain squad for the recent World Cup in Russia as back-up to David De Gea, but did not get any playing time.
Kepa signed a new long-term contract, which increased his release clause from 20 million euros, with Athletic in January to end speculation linking him with a move to Real.
The European champions are instead on the verge of completing a reported 35-million-euro deal for Courtois, who was voted the best goalkeeper at the World Cup.
Courtois, who spent three seasons at Atletico Madrid from 2011 to 2014, has repeatedly stated his desire to move closer to his two children in the Spanish capital.
However, Real coach Julen Lopetegui refused to comment on the speculation following his team's 2-1 victory over Roma in the final game of their US pre-season tour on Tuesday.
"I always say that I'm not talking about players who're not at Real Madrid," said Lopetegui. "Keylor (Navas) is our goalkeeper and there are no other goalkeepers I can talk about except Keylor, Kiko (Casilla), Andriy (Lunin) and Luca (Zidane).
"Keylor is phenomenal, he has our full confidence and is an extraordinary goalkeeper. He's delighted to belong to Real Madrid and we're delighted with him."