Leno fell out of favour at Emirates Stadium behind Aaron Ramsdale, making only eight appearances in all competitions, four coming in the Premier League.
The 30-year-old has penned a three-year contract with the Cottagers with a reported fee of eight million pounds. There is the option to extend another 12 months in the contract.
Leno had been expected to exit Arsenal, who also signed US shot-stopper Matt Turner this off-season.
“It feels amazing to finally be here. I cant wait to join the team, to train and play with the team,” Leno said.
“I’m relieved that everything is done. I’m just happy to be here. It took a little bit of time but in the end we made it, and that’s the most important thing.”
Fulham, who were champions in the Championship last term, have bolstered their squad with the additions of Kevin Mbabu, Andreas Pereira, Kristian Sekularac and Joao Palhinha. Manor Solomon has also joined on loan from Shakhtar Donetsk this week.
Marco Silva has also seen a few key players exit, including Fabio Carvalho who signed with Liverpool for five million pounds. Jean Michael Seri has also left for Hull City.
Leno will compete with Marek Rodak and Paulo Gazzaniga to be Fulham’s number one.
Fulham vice-chairman Tony Khan said: “Bernd Leno is the goalkeeper whom we have pursued steadfastly throughout this transfer window, and we’re very excited that we’ve reached a transfer agreement and he’s now fully committed to Fulham.”