Croatian boss Juric replaces Russell Martin, who was sacked following a 5-0 defeat at home to Tottenham last weekend.
"I'm very pleased. I think it's a really big challenge but I'm very optimistic because I saw a team that can do better," Juric said.
"It's important to immediately be connected with the fans. I want an aggressive team and I think that fans of Southampton will like that."
Juric, 48, is awaiting the approval of his work permit, meaning it is unlikely that he will be in the Southampton dugout for their match against Fulham.
Southampton said they hope the hiring of Juric will provide the "grit and determination" they need to overcome the threat of relegation amid a woeful first half of the campaign.
The Saints are bottom of the Premier League table with five points – nine off safety – through 16 games.
Juric was most recently the coach at Roma after replacing Daniele De Rossi but was sacked this season just 12 games into his tenure.