Adams is joining Mali winger Moussa Djenepo at Saints.
Hasenhuttl said: “Che fits the profile of player we want to bring to Southampton and is very driven to show what he can do at the highest level.
“We have been monitoring his progress for some time now. He has shown a desire to join us above all other clubs, which shows the positive reputation Southampton has built for developing young players.
“I am delighted to have signed Che and Moussa ahead of the start of pre-season. They are both young, dynamic players with the level of enthusiasm and hunger we are looking for that can help us improve as a team."