The 19-year-old, who has won six senior caps for his country, scored 11 goals in 34 appearances on loan at Vitesse in the Netherlands last season.
Broja signed a new five-year contract with Chelsea this summer and has impressed for the Blues in pre-season.
“Armando is a very talented player who we were impressed by last season,” said Southampton boss Ralph Hasenhuttl.
“He is young, but he comes now with a full season of experience in senior football with a good team, and he brings a lot of qualities that can help us.
“He is a strong, quick player with a good instinct and this makes him a good fit for the way we like to play.
“I know how highly regarded he is by Chelsea and I think this will be a good place for him to continue his own development as well.”
Broja said he is “excited” to be joining another Premier League club.
“Southampton have a good history and they play in the best league in the world,” he said.
“So it’s amazing for a young player to experience it, be in and around a Premier League team, and learn and develop from the older players, the staff and everyone here. It’s a very good opportunity.”
Saints begin their Premier League campaign away at Everton on Saturday, 14 August.
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