The 31-year-old Frenchman's contract at The Emirates expired this summer, and he leaves the north London club after 284 matches and seven years.
He has signed a three-year deal.
The full-back broke into the French national side during his time with Arsenal, and has 41 caps. He is currently in Brazil for the World Cup, where France face Honduras in their opening game on Saturday.
Sagna posted an emotional farewell message to Arsenal fans via Instagram on Thursday ahead of the expected move, and his transfer to the Premier League champions has now been confirmed.
"To be fair, i don't even know where to start or even how to say it... but i just wanna thank the whole Arsenal fc... a family to me," Sagna's message said.
"A club who taught me so much in 7years, a club where i had the chance to progress day by day, a club who always gave me his trust whenever i was personally not at my best...
"Of course i wanna thank the coach MR WENGER... who believed in me..gave me his trust..and clearly changed my life. Now, it's time for me to move on and one more time THANK YOU ."
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