Turner will wear the number 30 shirt at Arsenal, who have reportedly paid an upfront fee of $6m (£4.8m) which could rise to as much as $10m (£8.1m) with performance-related add-ons.
A deal between Arsenal and New England Revolution to sign Turner was agreed in the January transfer window, and the USA international arrives in North London to provide backup and competition for Aaron Ramsdale.
"He has shown with his performances in recent years in both the MLS and at international level with the United States that he is a goalkeeper who will give us added strength going into next season. We welcome Matt and his family to the club and we look forward to working together in the years to come."
Technical director Edu added: "We are delighted that Matt is joining us. Matt is a goalkeeper with established qualities and experience, who will be a great addition to our squad.
"We identified Matt some time ago and worked hard to ensure that his transfer was complete so he could join us in time for our pre-season in July. We now look forward to Matt joining us, settling into his new home and working ahead of next season."
Turner leaves New England after a six-year spell at the MLS club since arriving from Fairfield Stags, during which he kept 24 clean sheets in 111 appearances for the club.
The USA international made the MLS playoffs on three occasions with the New England outfit, reaching the semi-finals of the 2020 tournament before being eliminated by the Columbus Crew and winning the Supporters' Shield in 2021.
The shot-stopper has won 18 caps for the USA national team and played every minute for the Stars and Stripes en route to the 2021 Gold Cup crown, conceding only one goal in the process.
Turner - who was named the Revolution's MVP in 2020 - will also endeavour to establish himself as the USA's number one goalkeeper for the 2022 World Cup.
Turner's arrival in North London could open the door for Bernd Leno to leave the club in the coming weeks, with the German out of contract at the Emirates Stadium in 2023.
Leno played second fiddle to Ramsdale for the majority of the 2021-22 season, and the 30-year-old's agent has confirmed that Fulham hold an interest in signing him.
Following the signings of Turner, Marquinhos and Vieira, Arsenal are now expected to make Gabriel Jesus their fourth summer acquisition after reaching a £45m agreement with Manchester City. body check tags ::