The 24-year-old, capped 17 times by his country, will sign a three-year contract for an undisclosed transfer fee provided he is given entry clearance. He has already secured a work permit.
"To come to the Premier League was one of my biggest dreams since I was a child," Yoshida, who captained Japan in the 2012 London Olympics, said in a statement.
"I am very grateful to become a Saint. I want to show them what I can do as soon as possible."
Yoshida will join compatriot Tadanari Lee at St Mary's but it is likely he will need to wait to make his debut in England's top flight.
The stopper was on Thursday named in the Japan squad for a friendly against the United Arab Emirates next week and a 2014 World Cup qualifier against Iraq in Saitama on September 11.
Newly promoted to the Premier League, Southampton have lost both their opening games and face a daunting task against Manchester United this weekend.
Saints manager Nigel Adkins is eager to get Yoshida, scorer of last year's Goal of the Season in the Netherlands, into harness.
"We are delighted to bring Maya into the club," he told Southampton's website. "He is a centre-half who is comfortable on both the right and left-hand side. He has a good physical presence."
Yoshida is the second deal this week lined up by Saints after African Cup of Nations Golden Boot winner Emmanuel Mayuka and his Swiss club Young Boys agreed transfer terms.