The Journal reported that the data involved in the project includes lab results, doctor diagnoses and hospitalisation records, among other categories, and amounts to a complete health history, along with patient names and dates of birth.
Ascension "are the stewards of the data, and we provide services on their behalf," wrote Tariq Shaukat, president for industry products and solutions at Google Cloud.
In a press release, Ascension said the partnership is in compliance with the Health Insurance Portability and Accountability Act (HIPPA) which safeguards medical information.
Google Cloud Chief Executive Officer Thomas Kurian has made it a priority in his first year on the job to aggressively chase business from leaders in six industries, including healthcare.
The company previously touted smaller healthcare clients, such as the Colorado Center for Personalized Medicine.
Though cloud storage is a business with thinning profit margins, Google Cloud has said it hopes to separate itself from larger rivals Microsoft Azure and Amazon Web Services with a superior slate of high-margin AI tools.
Ascension said it aims to use AI to help improve clinical effectiveness as well as patient safety.
Google's blog post did not mention AI, but said the companies were in "early testing" on how to make better use of Ascension's data.
Google has spent several years developing artificial intelligence to automatically analyse MRI scans and other patient data to identify diseases and make predictions aimed at improving outcomes and reducing cost.
The news follows an earlier announcement from Google that it would buy Fitbit for $2.1 billion, aiming to enter the wearables segment and invest in digital health.