Nielsen, who had been at Benetton and then Renault as sporting manager since 2000, would join his new employers on December 12 to replace the departing Dieter Gass.
Owner Tony Fernandes said in a statement that team manager Graham Watson had also signed a new contract.
"It is a good mark of our team that we can attract people of Steve's calibre," he said. "I am thrilled that someone who is so well-respected, and is coming from a team that is ahead of us in so many ways, shares our belief in our ability to grow and in due course challenge the midfield."
The Renault-powered Team Lotus, who have yet to score a point since their debut last year as Lotus Racing, are changing their name to Caterham next season.
In a separate announcement, Renault said Jean-Michel Jalinier would take over as president of the French carmaker's F1 division from January 1 in place of Bernard Rey.
Renault are providing four teams with engines next year, having ceased to be a constructor with their former team becoming Lotus.
Meanwhile, Michael Schumacher, the seven-time world champion has caused a stir in Germany by insisting "Switzerland is the only home I have".
"Home is where we feel happy - and that's just on Lake Geneva," the Mercedes-GP driver told Swiss newspaper the Neue Zuercher Zeitung.