Aribo has signed on for the next four years at the Saint Mary's stadium for an initial £6m fee.
The 25-year-old spent three years at Rangers, having joined from Charlton Athletic in the summer of 2019.
He made 149 appearances for Rangers, scoring 26 goals and making 25 assists.
Aribo helped Rangers win the Scottish Premier League in the 2020/2021 season as well as the Scottish Cup last term.
Speaking to Southampton's official website on his arrival at the club, Aribo said: "It's an amazing club with a lot of history here, and it's a good plan with what's to come next. I'm really excited for the journey.
"The Premier League is the best league in the world. I've been watching it since I was a young boy, it's always been a goal for me to play here and show what I can do on this stage.
"It's an amazing feeling, a dream come true. This is where I've wanted to be since I was a child growing up playing, so to say that I'm here now is really exciting."
Southampton manager Ralph Hasenhuttl added: "Joe is a player with many qualities to his game, and we are very excited to welcome him to the squad in time for the pre-season trip to Austria.
"We believe Joe can bring energy and creativity to our side. Feeling comfortable in so many different positions is very helpful for a manager and shows he has a high level of football intelligence, with the ability to take on new information quickly.
"He has played a lot of games already in his career, at a very high level, and his performances in the Europa League prove he has the quality to play in the Premier League. This is a big ambition for him, and he is hungry to show everybody he can do it."
Aribo is Southampton's fifth summer signing.
