Ramsdale lost his place to David Raya last season, making just six appearances in the Premier League after the Spaniard's arrival in 2023.
The 26-year-old had been linked with Wolves but that move fell through and paved the way for his switch to St Mary's.
"I'm absolutely delighted. The way the manager wants to play, the way he was when I spoke to him, he was just full of so much enthusiasm," Ramsdale said.
"I'd never met him before, but he made me feel about eight feet tall, which is just what you want."
Ramsdale joined Arsenal from Sheffield United in 2021 and made 89 appearances in all competitions.
He was voted into the PFA's Premier League Team of the Year for the 2022/23 campaign, but was surprisingly axed to make way for Raya as Mikel Arteta looked to improve a team that eventually finished as runners-up to Premier League champions Manchester City for a second successive season.
Ramsdale's father was critical of the way the Arsenal manager handled the situation after the keeper was dropped.
Arteta still paid tribute to Ramsdale for his contribution during three years at the Emirates Stadium.
"Aaron has been a top professional since joining in 2021 and has made many contributions during his time with us," Arteta said.
"We thank Aaron for everything he gave to Arsenal and we wish him and his family the best of health, success and happiness in his new opportunity with Southampton."
Ramsdale will aim to get his career back on track at promoted Southampton, with his debut potentially coming against Brentford on Saturday.
Saints boss Russell Martin believes former Bournemouth keeper Ramsdale will be revitalised by his move.
"He is hungry to become England's number one again and he wants to be here. I think that is so important," Martin said.
"If you had asked me four or five weeks ago, 'Would we have had a chance of signing Aaron Ramsdale?' I would have thought you were probably crazy but then we've spoke a fair bit over that period of time.
"I think he has been frustrated over the last year at the lack of playing time, but he brings winning mentality, big character, big voice."
