Neither club disclosed the fee paid for the 21-year-old but the deal is reported to be worth in the region of €8 million (£7.1m/$9m).
A physically imposing forward, Saponjic will provide an extra attacking option for coach Diego Simeone alongside Diego Costa, Alvaro Morata and record signing Joao Felix, who also arrived from Benfica for €126m (£113m/$141m).
But while the Portugal international starred in the club's Primeira Liga triumph in the 2018-19 season, Saponjic played for Benfica B after joining from Partizan Belgrade in January 2016 and spent the 2017-18 campaign on loan with Belgian club Zulte Waregem.
He joins fellow new faces Marcos Llorente, Hector Herrera, Felipe, Lodi and Joao Felix at Atletico, with star forward Antoine Griezmann widely expected to complete a €120m (£107m/$135m) switch to Barcelona.
The 21-year-old Serb joined Partizan from Sloboda Uzice as a youth player in 2013, working his way up to the first team where he made his competetive debut in 2014.
He scored 11 times in 42 appearances for the Serb giants, starring as they won the Serbian Cup in 2015 and forcing his way into the under-21 side of the Serbian national team.
He failed to make an appearance in Benfica's first team after swapping Belgrade for Lisbon, but managed to net eight times in 40 appearances for the B team before loaned out to Belgium in 2017.
His chances of making the first team at the Wanda Metropolitano will be boosted if Griezmann finally makes his long-awaited move to Camp Nou in the coming weeks, with the France World Cup-winner believed to have agreed terms to move to the Liga champions.
Last season's runners up Atletico are looking to make up an 11-point gap to Barca next term, as they aim to win a first league crown since Simeone guided them to a shock title success in 2014.