Adams scored 22 goals and notched six assists for an embattled Birmingham side last season and was shortlisted for the Championship Player of the Year, making the Team of the Season at the EFL Awards.
Saints signed the 22-year-old striker on a five-year contract but the transfer fee is undisclosed.
“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,” Saints manager Ralph Hasenhuttl told the club website.
“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.”