Hasenhuttl confirmed that the Frenchman has signed following their 2-0 win over West Brom on Sunday.
"It's done. He's our new player," Hasenhuttl confirmed to BT Sport.
"We are happy that we have him here and hopefully we get another one in. I think with two more players it looks okay."
When asked who else the Southampton boss is looking to bring in, Hasenhuttl smiled and said: "I will tell you in the next 24 hours hopefully."
The Saints have already made Kyle Walker-Peters loan a permanent switch from Spurs, signing the full back for £12m.