Sky Sports revealed over the weekend that Ronald is set to take charge at St Mary's, and his appointment is now imminent.
The former Netherlands international will become head coach and his older brother Erwin will be his assistant.
The duo boast extensive managerial experience, with Ronald having managed the likes of Ajax, Benfica, PSV Eindhoven, Valencia and most recently Feyenoord.
Like his brother, Erwin has spent plenty of time in the dugout with Feyenoord, Utrecht, the Hungarian national side and RKC Waalwijk - who he left this summer.
Ronald’s representative Guido Albers told Voetbal International: “He wants to make a next step in his career at an ambitious club with possibilities. Southampton fits in that profile.
"Pochettino made a solid base and Ronald is the ideal candidate to build the squad from there.”
Kees Ploegsma, the agent to Erwin, added: “It’s correct that there are talks. They want Ronald to be manager and his brother Erwin as his assistant.”
Saints are already being linked with a number of players with Dutch links, with Feyenoord duo Lex Immers and Graziano Pelle and Celtic defender Virgil van Dijk said to be high on the Koemans' wanted list.
Watch Sky Sports News from 9am this Wednesday for the announcement of next season's Premier League, Football League and SPFL fixtures.