The 23-year-old France worldwide flew to Los Angeles to undergo a medical and compete the deal on Sunday ahead of joining-up with City's pre-season tour of the United States.
"We've replaced some key players in the team that did a lot of good over the years", Kompany added.
All four of Man City's full-back options last season - namely Aleksandar Kolarov, Gael Clichy, Bacary Sagna and Pablo Zabaleta - have either been sold or released, making the position a key area for recruitment.
Chelsea's Pedro returns to London after suffering concussion
I repeat, we are a great club but we are in a moment where we can't make a mistake because it's very unsafe . I would be surprised if someone was surprised about my decision now".
Mendy quickly managed to establish himself as one of the best full-backs in world football with his powerful and direct style of play.
The France global left back is Guardiola's sixth signing - and third new full-back - of a whirlwind summer following his £52m move from Monaco. I don't really wait for it to happen, I get out there and pass on the message I think is the most appropriate when I'm on the pitch.
The deal is reported to be worth in the region of £50million, ($82M) a similar fee to the one City agreed to bring in England right-back Kyle Walker from Tottenham.
"I'm sure he will prove a fantastic addition to the squad".
The Citizens are desperately looking for a buyer as Pep Guardiola made clear he no longer figures in his plans at the Etihad. Walker showed in City's preseason derby loss against Manchester United in Houston that he is able to supplement the attack and still have the energy levels to cover someone as fast as Marcus Rashford.