The 22 year-old was coveted by a number of top European clubs, and it is Saints who have won the race for his services.
Mané joins from Austrian champions Red Bull Salzburg, where he scored 45 goals in 87 appearances after moving from French side Metz two years ago.
The wide-man has 15 caps and three goals for his country, and was in the Senegal squad at the 2012 Olympic Games. He is currently on international duty, and will be presented as a Southampton player upon his return.
First Team Manager Ronald Koeman said: “Right from the first meeting I had with Les Reed, when it was clear that we would have to change a lot, Sadio was on our list of potential players.
“I know the player because last season Ajax Amsterdam played against Red Bull Salzburg in Europe, and I saw him playing and I was impressed with his qualities and with the physicality that he showed.
“He can play in different positions in the attack – he can play on the left or right side and also as a number nine. It is incredible how many goals he has scored from his position, and I hope that he will do the same for us.
“With the way that we play and the fact that I know him very well, this is a good step forward for him.”