German newspaper Bild is now joining specialist outlets in reporting that the 29-year-old has signed a three-year contract.
Reportedly, Hulkenberg could earn €18m (£16.3m) over the course of the agreement, which is actually a two-year deal including an option for 2019.
Magnussen told Danish business newspaper Dagbladet Borsen that playing the political game in F1 is not his strength.
"I'm really bad at the political game," said the 24-year-old, who also lost his McLaren seat after one season after making his grand prix debut in 2014.
"I'm a racing driver, not a politician, so I don't try to go out and get voters on my side. I'm here to race and drive fast, which is what I enjoy and what I feel I'm good at."
Magnussen, whose father Jan also had a short-lived career in F1 in the 1990s, also admitted that he struggles with the nomadic lifestyle.
"Every time I leave my family I think 'Is it worth it?' It's hard to be away so much," he added.
"But when you are not winning, and things are not going as you would like, as is the case right now, you have those thoughts more often. But if one day I stand at the top of the podium, I will know it was all worth it."
The 2016 championship continues next weekend with the United States Grand Prix.