Sauber will be rebranded as Alfa Romeo Racing from the start of the 2019 season.
Alfa Romeo was last on the Formula 1 grid as a constructor in 1985 but returned to the sport last season as Sauber's title sponsor.
The Swiss team say the ownership and management structure remains unchanged but the Sauber name will disappear.
Sauber has been a fixture in F1 since in 1993, when team boss Peter Sauber made the switch from sports car racing.
Kimi Raikkonen, the 2007 world champion, and Antonio Giovinazzi will race for the rebranded outfit, which finished eighth in the constructors' championship last season and will again be powered by Ferrari engines in 2019.
Team principal Frederic Vasseur said: "After initiating the collaboration with our title sponsor Alfa Romeo in 2018, our team made fantastic progress on the technical, commercial and sporting side. This has given a boost of motivation to each team member.
"We aim to continue developing every sector of our team while allowing our passion for racing, technology and design to drive us forward."
The Italian car manufacturer dominated the early years of F1, with Giuseppe Farina winning the inaugural world title driving an Alfa in 1950, before Juan Manuel Fangio claimed the first of his five titles racing for the team a year later.
Alfa will roll out their 2019 car on the first morning of pre-season testing, which gets under way in Barcelona on 18 February.
Chief F1 writer - Andrew Benson
The renaming of the Sauber team as Alfa Romeo may on the one hand be a rebranding exercise for marketing purposes, but it is also a seminal moment in Formula 1 history.
It marks the first time an F1 team will be solely named after the iconic Italian manufacturer since 1985 - and the first time the Sauber name will not be on the grid since 1993.
Both entities have carved a unique place in motorsport history.
Alfa Romeo were a major force in grand prix racing between the wars, spawned Ferrari and won the very first F1 world championship in 1950, even if their history in the sport has been somewhat less illustrious after they faded away in the mid-1950s.
Sauber, for their part, first entered F1 as a proxy for Mercedes, with whom they had previously had a successful period in endurance racing.
After Mercedes joined McLaren in 1995, Sauber went it alone, before joining forces with BMW from 2006-9, and then becoming independent again. They had just weathered a difficult financial period before heading back up the grid in 2018 after the Fiat Group made investment in the team following the decision for the cars to carry the name of its Alfa Romeo brand.
Those links have just become stronger still, and they suggest the now-renamed Alfa Romeo team could continue the upward progress seen last year most obviously in the starring performances of Charles Leclerc, who is now at Ferrari.
Politically, it is also an important move. It further enhances the team's status as a Ferrari B team - already evidenced by Leclerc's promotion and the presence of Italian Antonio Giovinazzi in the car this year alongside ex-Ferrari veteran Kimi Raikkonen.
In addition to Ferrari's strong relationship with Haas, that increases the company's strength as negotiations over the sport's future beyond 2020 enter a critical phase this year.