The Germany international was signed for a £22.5m fee from Bayer Leverkusen in the summer of 2018 and competed with Petr Cech for the number one spot during the 2018-19 season.
Leno soon became Unai Emery's number one and held his place under Mikel Arteta, despite Emiliano Martinez's trophy-winning exploits during his time on the sidelines.
Martinez left the club when Leno retained possession of the gloves in 2020, but the arrival of Aaron Ramsdale pushed the 30-year-old down the pecking order last season.
Furthermore, the Gunners have added Matt Turner to their goalkeeping ranks for the 2022-23 season, which saw Leno drop to third choice at the Emirates Stadium.
With Leno due to become a free agent in the summer of 2023 and the World Cup looming, the shot-stopper was expected to complete a permanent move elsewhere to boost his chances of making Hansi Flick's Germany squad.
Arsenal have now confirmed the departure of Leno to Fulham, writing on social media: "A model professional. A credit to The Arsenal. Thank you for everything and good luck, Bernd ❤️"
During his time in North London, Leno kept 37 clean sheets from 125 appearances in an Arsenal shirt and was a part of the Gunners' 2020 FA Cup and Community Shield winning squads, but he did not play in either final.
The German shipped nine goals in three games against Brentford, Chelsea and Manchester City in the Premier League last term and only made one further top-flight appearance for the club in a 1-0 success over Aston Villa in March.
Arsenal were initially reported to have agreed an £8m fee for the transfer of Leno, but a report from The Athletic states that the full price will only be met if specific add-ons are hit.
Fulham will supposedly pay just £3m up front for the 30-year-old's services, which should rise to £4m during the season based on his Premier League appearances.
The Gunners will then receive a further £2m if Fulham remain in the Premier League for the 2023-24 season, and an identical amount if the Cottagers can stay up for a third season.
Leno paid tribute to Arsenal fans on Instagram in a goodbye message, posting: "Hey Arsenal fans, It's time to move on for me. It's been a pleasure to be part of this great football club for 4 amazing years.
"Thank you very much for your support. Also a big thank you to my team mates and the staff behind the team. I'm looking forward to see you soon at the Emirates ❤️