Yoshida, a 24-year-old central defender who played with Dutch side VVV Venlo last season, has already been granted a work permit by the Home Office and his papers are expected to be completed on Friday.
The transfer fee is reported to be worth ?2million (2.5million euros)
"I am very grateful to be able to become a Saint and I will do my best for the team and for the supporters," he told the club's website.
"I saw a video of the recent history of Southampton since the takeover, which showed me the great supporters when the club was promoted last season.
"I want to show them what I can do as soon as possible and hopefully impress them with my performances."
Yoshida will have to wait before meeting up with his new team-mates at St Mary's as he is on international duty with his country having been named in the Blue Samurai's squad for a friendly match in preparation for their Asia Zone World Cup qualifier against Iraq in Saitama on September 11.
"We are delighted to bring in Maya to the club," Saints coach Nigel Adkins said.
"He is a centre-half who is comfortable on both the right and left-hand side as he is good with both feet and has a good physical presence about himself.
"We are really looking forward to working with him here at Southampton."
Yoshida was captain of the Japanese Olympic team that took fourth place in London earlier this month.
Southampton won promotion to the Premier League last season after several years out of the top flight, but they lost their opener 0-2 to Wigan at home last weekend.