Safri, who missed training on Monday and was late for the annual squad photo, had incurred the wrath of his occasionally terrifying manager Grant.
The Scotsman has maintained that any member of playing or coaching staff who is less than fully committed to the cause is welcome to leave, and has stayed true to his word.
Safri, 30, who signed from Coventry, moves to St Mary's for an undisclosed fee. He is likely to miss a chunk of the New Year programme on African Nations' Cup duty with Morocco.
The 'Moroccan all over the world' will be best remembered in Norfolk for his exocet shot into the top corner of Shay Given's goal in a 2-1 win over Newcastle.