Sulemana joined Rennes from Danish club Nordsjaelland in 2021 and has played 20 times this season, scoring once and providing two assists.
Saints have also signed striker Paul Onuachu, 28, from Genk until 2026.
BBC Radio Solent reported that the deal for Sulemana, who has won 15 caps for Ghana, could rise to £24.6m.
It exceeds the £20m Saints paid to sign Danny Ings from Liverpool in 2019.
Sulemana made three appearances at the World Cup in Qatar and was recorded running at 35.7kph (22.2mph) during the tournament, the quickest speed of any player.
“This is another really positive addition for us this month. We have been keen to add a little more potency to the side and Kamaldeen does that for us,” manager Nathan Jones said.
Onuachu is the leading scorer in the Belgian top-flight, having scored 17 goals in 22 appearances.
He has made 16 appearances for Nigeria, scoring three times.
Credit: BBC Sport
