The FAA has issued an advisory circular that provides aircraft owners, operators, and pilots operating aircraft under Title 14 of the Code of Federal Regulations (14 CFR) part 91, with information for removal of paper aeronautical charts and other documentation from the cockpit through the use of either portable or installed cockpit displays (electronic flight bags (EFB)). It can be found at this link.
It references AC 120-76A that defines the EFBs that it references.
It’s not very long so you should read it, but the relevant part is as follows:
The in-flight use of an EFB/ECD in lieu of paper reference material is the decision of the aircraft operator and the pilot in command. Any Type A or Type B EFB application, as defined in AC 120-76A may be substituted for the paper equivalent. It requires no formal operational approval as long as the guidelines of this AC are followed.