The 21-year-old, who was the top scorer at the African Cup of Nations as his Zambia side claimed a shock victory, striker passed a medical, Saints said, and has been granted a work permit.
The club hopes the deal can be ratified in time for Mayuka to join Saints for their clash with Manchester United on Sunday.
"Emmanuel is a lightning-quick striker who I am sure will excite the fans," Southampton manager Nigel Adkins said on the club's website.
"He is only 21-years-old but already has a great deal of experience, notably so at international level."
Mayuka has been capped 36 times since making his international debut in 2007. Three of his 10 goals for Zambia came in the 2012 African Nations Cup, which his country won for the first time.
Mayuka was one of seven players to score three times in the tournament but was awarded the top goalscorer's Golden Boot by virtue of an extra assist.
Premier League new boys Southampton, without a point from their first two league matches, are also hopeful of signing Uruguayan winger Gaston Ramirez from Italian side Bologna.
- Sports & Recreation