Alexander was centrally involved at McLaren for more than 40 years after being recruited by driver Bruce McLaren to help set up the team in 1963.
He left in 1983, two years after McLaren was taken over by current boss Ron Dennis, but returned in 1989 and worked there until he retired in 2008.
"Tyler was one of the first pillars of our company," said Dennis.
"Bruce couldn't have asked for a sturdier pair of shoulders upon which to help build the team's reputation. Quite simply, Tyler lived and breathed McLaren."
In the early years of the team, Alexander worked alongside Bruce McLaren and fellow American Teddy Mayer in F1, first as chief mechanic and then chief engineer before becoming a director of the company.
The company continued under Mayer following McLaren's death in a testing crash in 1970.
In the late 1960s, Alexander moved to run the company's successful programmes in the US, first in the CanAm sportscar championship and then in Indycar racing, before returning to F1 in 1979.
Dennis took over McLaren in 1981, first running it alongside Mayer before taking total control, and two years later Alexander sold his shares to Dennis and left the company.
He returned to the US to join Mayer in running an Indycar team, which recruited as engineer a young Adrian Newey, now Red Bull's chief technical officer and the most decorated design engineer in F1 with world titles at Williams, McLaren and Red Bull.
Alexander and Mayer were the joint team principals of the short-lived US-based F1 team Beatrice in 1985 and 1986. After its collapse, Alexander returned to Indycar racing before Dennis re-signed him as McLaren's special projects engineer in 1989.
During his final 20 years with the company, McLaren won six drivers' and five constructors' world titles with Ayrton Senna, Mika Hakkinen and Lewis Hamilton.
In a tribute to Alexander on the McLaren website, Dennis said: "Tyler was one of the finest of the old school: hardy, humble and wise, leaving a reputation and a legacy that will remain indelible in the history of international motorsport."

The Scots, who top their Euro 2017 qualifying group, host nearest challengers Iceland on Friday evening.
Midfielder Little, 25, recently won the BBC Women's Footballer of the Year award and is likely to play a key role for Signeul at the Falkirk Stadium.
"It is a really well deserved award for Kim," said Signeul, whose team have five wins from five in Group One.
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"Every team in the world would like Kim Little in their team. She is such an ambassador for the game and she is a role model for all young girls in this country.
"She is an amazing player and person. She will be very important for us."
Signeul believes four points from the next two qualifying games will be enough to secure Scotland's place at their first major finals.
After facing Iceland, they will travel to play Belarus on Tuesday. Their final qualifier, away to Iceland, is in September.
Like Signeul's side, Iceland have a 100% record in qualifying, but the Scots have played a game more.
"It is a chance for us to show how good we are, a chance for us to qualify for the Euros," said Signeul.
"We have two games coming up. We need four points to actually qualify. That is what our aim is.
"If we win tomorrow against Iceland, that would be fantastic. However, re-focus, go to Belarus and win there and then we can relax a little bit.
"Iceland are a very strong team. They are physical, tactically very good like their men's team, and technically very good, so it will be a really tough game.
"However, we have a good squad. We have good players, who are also physically very good - maybe not as tall - but who are starting to get taller in the squad.
"I definitely think that we look very good."

The body of Christopher Butler, 27, from Southsea, was discovered at a flat in Waverley Road in the early hours of Friday.
A 23-year-old woman and a 33-year-old man, both from Portsmouth, are being held, Hampshire Constabulary said.
A post-mortem examination on Friday was inconclusive.
American Tyler Alexander, one of the key figures in the founding of the McLaren team, has died aged 75.
[NEXT_CONCEPT]
Scotland women's coach Anna Signeul believes any team in the world would want Kim Little in their starting XI.
[NEXT_CONCEPT]
Two people have been arrested on suspicion of murder following the death of a man in Portsmouth on New Year's Day.