According to British media reports, Arsenal paid Brentford a loan fee worth £3 million for Raya and will have the option to sign the goalkeeper on a permanent basis for £27 million.
Raya has made over 160 appearances for Brentford since joining the club in 2019, playing a key role in their promotion from the second-tier Championship in 2021.
He also has two caps for Spain, making his debut in 2022 and travelling to Qatar as part of their squad for the World Cup.
"David is a top-quality goalkeeper, who has consistently performed to a high level with Brentford in the Premier League," Arsenal sporting director Edu said.
"With David joining us we are adding quality and depth to our squad so we can perform at the highest possible level in all competitions."
Brentford added that Raya had signed a two-year contract extension before moving to Arsenal.
The West Londoners, who finished ninth in the Premier League last season, signed Dutch goalkeeper Mark Flekken from Bundesliga side Freiburg on a four-year contract in May.
Arsenal next travel to face Crystal Palace, while Brentford take on Fulham.