Google is engaged with one of the U.S.’s largest health-care systems on a project to collect and crunch the detailed personal-health information of millions of people across 21 states.

The initiative, code-named “Project Nightingale,” appears to be the biggest effort yet by a Silicon Valley giant to gain a toehold in the health-care industry through the handling of patients’ medical data. Amazon.com Inc., Apple Inc. and Microsoft Corp. are also aggressively pushing into health care, though they haven’t yet struck deals of this scope.

Google began Project Nightingale in secret last year with St. Louis-based Ascension, a Catholic chain of 2,600 hospitals, doctors’ offices and other facilities, with the data sharing accelerating since summer, according to internal documents.

The data involved in the initiative encompasses lab results, doctor diagnoses and hospitalization records, among other categories, and amounts to a complete health history, including patient names and dates of birth.

Neither patients nor doctors have been notified. At least 150 Google employees already have access to much of the data on tens of millions of patients, according to a person familiar with the matter and the documents.