Nielsen, who has most recently worked for Formula One Management (FOM), has had a lengthy career in grand prix racing which included spells at Lotus, Tyrrell, Benetton and AlphaTauri.
In his new role at the FIA, he will be responsible for all sporting matters, including the development of race control and the remote operations centre, as well as future updates to the sporting regulations.
Speaking about his new role, Nielsen said: “I have spent my professional life working for many teams and organisations in Formula 1, and cannot wait to engage with another new chapter with the FIA.
“I’d like to thank both the president and Stefano Domenicali for their trust in me, and I understand and appreciate the unique challenges that come with being the regulator.
"Having worked closely with a number of people in the federation over the years, I’m looking forward to tackling those challenges that lie ahead with them - Formula 1 is in a great place at the moment, and it’s our responsibility to ensure the future health of the sport that is at the heart of everything we do.”
Nielsen’s appointment is one of a number of changes that FIA president Mohammed Ben Sulayem has introduced to help better run F1.
Nikolas Tombazis, who has led the FIA’s technical team in F1 since 2018, will have a new more senior role as single-seater director.
Reporting to him will be Nielsen, technical director Tim Goss, financial director Federico Lodi and operations director Francois Sicard.
Ben Sulayem believed the changes would help improve the FIA’s running of F1.
He said: “We have dedicated a lot of time and effort to making significant, informed changes to our Formula 1 team to create the right structure with the right people to oversee the future regulation of the sport.
“By developing and empowering people within our organisation, as well as bringing in expertise and experience from the outside, I am confident that we are in the best position possible to move forward together with our partners at FOM and the Formula 1 teams.”