Campos Racing, who have teams in the Formula Two and Three support series, said in a statement on Thursday that their founder had passed away from "sudden coronary disease".
"His heart stopped beating, but his memory will be the engine that will keep us all fighting to continue his legacy," they added on Twitter.
Campos started 17 grands prix in 1987-88 without scoring a point.
He then focused on running teams in the junior series, working with future F1 drivers Marc Gene and Alonso early in their careers.
"One of the saddest days for the motorsports family," said Alonso on Twitter. "Driver and great promoter of this sport. Thank you for dreaming about Formula One. Thank you for believing in young people. Thank you and rest in Peace."
Ferrari driver Carlos Sainz hailed Campos as "a benchmark of our sport in Spain and internationally."
Formula E founder Alejandro Agag, who bought the Campos GP2 team in 2009, thanked his compatriot for bringing him into racing.
Britain's Jack Aitken, the Williams reserve who made his grand prix debut in Bahrain as a stand-in last year, raced for the Campos F2 team in 2020.
In 2009 Campos had a bid to enter a Campos Meta team in Formula One accepted but financial problems saw it change ownership and compete as Hispania, later HRT F1.
The team, who gave Australian Daniel Ricciardo his F1 debut in 2011, folded at the end of 2012.
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