The USA international, who turned 21 this week, arrives for a fee of around £6.8million, after helping fire FC Koln to the 2.Bundesliga title in May.
The forward scored 10 league goals in 29 appearances last campaign, and has averaged a goal every 164 minutes in his senior career.
Six-foot four-inch Downs underwent his medical at Staplewood on Tuesday, following USA’s defeat to Mexico in the Gold Cup final on Monday.
After signing his deal, Downs said: “Everybody plays football to win titles. To win my first title at 20 last year was a great feeling, and I hope to repeat it again this year.
Saints signing Damion Downs pictured at Staplewood (Image: Southampton FC)
“I think Southampton is a big club that should be in the Premier League, and that’s my goal – to help the team as much as I can to bring the club back to the Premier League.”
Downs was born in Bavaria and represented Germany at under-20 level but holds dual citizenship, having been raised in two countries.
Downs recently earned his first senior international call-up from former Saints boss Mauricio Pochettino and made four Gold Cup appearances.
He scored the winning penalty in the quarter-final shootout win over Costa Rica, as USA reached the final only to lose out to Mexico.
At club level, Downs broke through from FC Koln’s second team during the previous campaign and scored two Bundesliga goals as a substitute.
Technical director, Johannes Spors said: “Damion is a player we have been monitoring for some time and possesses excellent physical qualities and the ability to disrupt defences.
“Strengthening our attacking options was one of our top priorities this summer, and Damion is a player who will add real quality to the group.
“Despite his relatively young age he is already a senior international, so we are excited to see him thrive in the environment here at Southampton.”