The 25-year-old made 128 appearances during his time at the Etihad, and also claimed 52 caps for his nation.
The left-sided player can operate in defence and midfield, and arrives at the Emirates having won the Premier League and League Cup four times.
Zinchenko also claimed the FA Cup and reached the Champions League final in 2021.
Speaking about the signing, Arsenal boss Mikel Arteta said: "We're so happy Alex has joined us. He's a player that I personally know really well and continued to follow him after my time at Manchester City.
"Alex is a high quality player who will give us options and versatility. It's not only about the positions he can play but as well, the versatility he will give us in attack and defence.
"Alex is a person with great human qualities and character, and I'm delighted that everyone has made this huge effort to bring Alex to the club."
Arsenal's Technical Director Edu added: "I'm very pleased to see how we're working as a team here in the club. We put a plan together early and Oleksandr Zinchenko was a main focus on our list.
"We're pleased to have Alex with us now because he has the attributes which I'm sure are going to put our squad at a different level."
Zinchenko becomes the club's fifth new signing of the summer, joining Marquinhos, Matt Turner, Fabio Vieira and former Man City striker Gabriel Jesus.
The player has already linked-up with the squad for pre-season training in Orlando.
The Ukraine international could make his first appearance in one of the two remaining friendlies against Chelsea and Sevilla.