The Spaniard had suffered massive head injuries and lost her right eye when she collided with a team support truck during a straightline test at Duxford Aerodrome in July 2012.
De Villota, who was 33, was found dead in a hotel room in Seville on Friday morning.
She had recovered from her injuries sufficiently to undertake extensive charity work, as part of which she attended this year's Spanish Grand Prix, and was due to launch her autobiography on Monday.
A statement read by de Villota's sister Isabel said the family had been informed that her death was a legacy of her injuries last year.
"Maria left us while she was sleeping, approximately at 6am, as a consequence of the neurological injuries that she suffered in July of 2012, according to what the forensic doctor has told us," said the family statement.
"Maria is gone, but she has left us a very clear message of joy and hope, which is helping the family move on in these moments."
She will be buried in Madrid "in the most strict intimacy."
A former sportscar and touring car racer, de Villota eventually focused on single-seaters. She competed in the Superleague Formula and tested a 2009 Renault for Lotus in 2011 before becoming Marussia's test driver last season.