The 40-year-old joined Saints last month as a free agent on a short-term deal following injuries to fellow keepers Alex McCarthy and Fraser Forster.
He made his debut in the 3-0 Premier League defeat at Arsenal on 11 December and also played in the 2-2 draw at Crystal Palace four days later before being an unused substitute in the club’s last two games after Forster returned to fitness.
Southampton boss Ralph Hasenhuttl told the club website: “Willy is a fantastic character who has freshened up our goalkeeper group massively.
“With the experience he brings, he is absolutely an important part of that group, and that was the reason we wanted to convince him to stay with us until the end of the season, and I am very happy he has decided to do this.”
Former Manchester City and Chelsea player Caballero has been capped five times by Argentina.
“I have really enjoyed my time here so far and I am very pleased to be able to stay for the rest of the season,” he said.
“There is a very positive atmosphere here. It has been good to work with the rest of the goalkeepers, and I hope I can continue to help the team in the coming months.”