Magnussen, who replaces the outgoing Pastor Maldonado, will race alongside Jolyon Palmer at the rebranded Renault Sport F1 Team, with GP3 racewinner Esteban Ocon joining as third and reserve driver.
In a ceremony streamed live from the French manufacturer's technocentre in Paris, Renault also became the first team to take the covers off their 2016 challenger, the R.S.16.
The new car, which was manufactured at the team's Enstone base, features a predominantly black livery, though Renault Sport chief Jerome Stoll hinted the colour scheme could change ahead of the 2016 season opener in Australia.
The car will be powered by Renault's R.E.16 power unit, which will continue to be developed in Viry-Chatillon.
Alongside Magnussen and Ocon, Renault also confirmed that Bob Bell will return to Enstone as chief technical officer, with Nick Chester becoming the chassis technical director and Remi Taffin the engine technical director.
Cyril Abiteboul, managing director of Renault's racing group, said the trio would help Renault hit the ground running in 2016.
"The ambition is not just to participate: we have no intention just to make up the numbers," Abiteboul said. "We are here to win. We have won in every category, there is no reason we cannot repeat that in F1. We know the way."
Newly appointed racing director Frederic Vasseur, who will report to Abiteboul, added: "Renault have proven in the past they can achieve and do it. Motorsport is a part of the DNA of Renault, and the motivation is more than high. We have a new challenge in front of us, and we are determined. For everybody - the drivers, the team, the engineers - the group is behind us and we have their full support."
Renault also announced the launch of a new driver academy, created with the aim of nurturing future F1 stars. The French manufacturer has a strong pedigree of driver development, having supported the likes of Robert Kubica, Heikki Kovalainen and Romain Grosjean in recent years. Formula Renault 3.5 champion Oliver Rowland is among the first wave of new inductees.