Koeman has finally completed a move to fellow Barclays Premier League side Everton after several days of talks and his old club have begun the search for his replacement
The former Dutch international joined Saints in 2014 and led the club to a sixth place finish in the 2015/16 season
Frank de Boer is believed to be the favourite to take over at St Mary's but Eddie Howe, David Moyes, Manuel Pellegrini and Ryan Giggs and also in the running
A statement on Southampton's official website said: " The search has already begun for the right appointment who can take the club to the next level and build on our track record of recent success, which culminated in a sixth place finish in last season's Premier League, as well as qualification for the group stages of the Europa League
"Our focus now is to build on our long-term plan, and work with a new management team who share both the club's and our supporters' values and ambitions."
Source : PA