Growing up in the American northwest, Nichols bought a go-kart with pocket money at age fourteen; his parents, hoping to channel the habit safely, gave him a proper racing go-kart, inadvertently deepening his interest in motorsport. A 1962 Road & Track article about the Lotus 25 — which the piece called "Chapman's Tubeless Wonder" — convinced the fifteen-year-old to pursue Formula One car design and shape his education accordingly. He graduated from the University of Utah in 1972 with a mechanical engineering degree.
Rather than join racing immediately, Nichols spent four years as a development engineer at Hercules Aerospace in Salt Lake City, where his team worked on stage-three rockets for Trident missiles used by United States Navy nuclear submarines. He then moved to Gabriel Shock Absorbers, helping the company break into motorsport by designing dampers eventually used by Al Unser, Parnelli Jones, Team Penske, and A. J. Foyt on the USAC Indycar circuit. During this period he encountered English designer John Barnard at Chaparral, a relationship that would prove decisive.
In mid-1980, Nichols joined McLaren in Formula One following an introduction through Barnard, who was then merging his Project Four Racing operation with McLaren under Ron Dennis. A significant early contribution came from Nichols suggesting his former employer Hercules Aerospace as the manufacturer of Barnard's revolutionary carbon fibre monocoque for the McLaren MP4/1 — Hercules had years of experience with carbon fibre in aerospace and accepted the work, also gaining a team sponsorship slot in return.
In 1982, Nichols became race engineer for Niki Lauda. He remained Lauda's engineer through the 1984 championship season, when Lauda defeated younger teammate Alain Prost by the smallest margin in Formula One history — half a point. After Lauda retired following 1985, Nichols moved to engineer Keke Rosberg in 1986 and Stefan Johansson in 1987.
When John Barnard departed for Ferrari after 1986, Ron Dennis appointed Nichols as chief designer. His first car, the McLaren MP4/3, was powered by a turbocharged TAG-Porsche V6 and carried Alain Prost to three victories in 1987, including the Portuguese Grand Prix where Prost claimed his 28th win, surpassing Jackie Stewart's long-standing record of 27. McLaren finished second in the Constructors' Championship behind Williams.
Nichols' second car as chief designer was the McLaren MP4/4, fitted with a turbocharged Honda V6. Driven by Ayrton Senna — whose race engineer Nichols also was — and Alain Prost, the MP4/4 won fifteen of sixteen races in the 1988 season. The only defeat came at the Italian Grand Prix, won by Gerhard Berger's Ferrari. McLaren won the Constructors' Championship by a then-record margin of 134 points over Ferrari; Senna took the Drivers' title, his first.
A longstanding dispute surrounds the design credit for the MP4/4. Gordon Murray, who became technical director in 1987, has claimed the car was substantially derived from his earlier Brabham BT55. Nichols, supported by other McLaren personnel including monocoque project leader Matthew Jeffreys, aerodynamicist Bob Bell, and engineer Alan Jenkins, has maintained that the MP4/4 was a development of the MP4/3 and that Murray had little involvement. Internal McLaren memos written by Murray himself record Nichols as chief designer of both the MP4/3 and MP4/4.
After the MP4/4, Nichols also engineered Senna for the 1989 season.
At the end of 1989, Alain Prost invited Nichols to join him at Ferrari. The team ran the Ferrari 641 in 1990, a development of John Barnard's semi-automatic-transmission Ferrari 640. Prost won five races and led the championship until a collision with Senna at the Japanese Grand Prix ended his title hopes. Nichols assumed the technical director role at Ferrari after Barnard departed and collaborated with chief designer Jean-Claude Migeot on the Ferrari 642 and 643 used in 1991. The 643 proved difficult to drive — Prost publicly called it harder to handle than a truck before being dismissed by the team — and the season produced no victories. Nichols left Ferrari in December 1991.
He subsequently helped Peter Sauber's team enter Formula One, then moved to Jordan as chief designer in 1993. In 1995 he returned to McLaren as a technical consultant, assisting the team's return to competitiveness that culminated in Constructors' Championships in 1998 and 1999. In 2001 he joined Jaguar Racing as technical director, delivering the team's first podium at the Monaco Grand Prix before leaving in early 2002. He has not worked in Formula One since.
In retirement, Nichols works as a freelance design and technical consultant based in the United Kingdom and races historically — a Datsun 260ZX and a Van Diemen RF82 in Historic Formula Ford 2000. In 2017 he founded Nichols Cars to produce the N1A, a road-going interpretation of the McLaren M1A race car.