The 21-year-old has signed a five-year deal at St Mary's after passing a medical with the newly-promoted Barclays Premier League side on Tuesday.
Mayuka has already been granted a work permit and Saints are now awaiting entry clearance for the deal to be fully ratified, which is expected to happen before the end of this week.
Mayuka joined Maccabi Tel Aviv from his first club Kabwe Warriors four years ago before signing for Young Boys in 2010.
Saints manager Nigel Adkins is looking forward to working with the pacy 5ft 9in attacker, who is the club's fifth signing of the summer.
'Emmanuel is a lightning-quick striker who I am sure will excite the fans,' Adkins told Southampton's website.
'He is only 21 years old but already has a great deal of experience, notably so at international level.
'He will bring something different to the group that we already have here at Southampton, and I look forward to seeing him pull on our shirt for the first time.'