The relevant paragraphs regarding this new 60-day grace period from the Federal Register:
"Under the final rule, DHS may also authorize a grace period of up to 60 days in the E-1, E-2, E-3, H-1B, H-1B1, L-1, and TN classifications during the period of petition validity (or other authorized validity period). See final 8 CFR 214.1(l)(2). In response to public comments, DHS is retaining this provision while adding the O-1 visa classification to the list of nonimmigrant classifications eligible for the 60-day grace period. To enhance job portability for these high-skilled nonimmigrants, this rule establishes a grace period for up to 60 consecutive days, or until the existing validity period ends, whichever is shorter, whenever employment ends for these individuals. The individual may not work during the grace period. An individual may benefit from the 60-day grace period multiple times during his or her total time in the United States; however, this grace period may only apply one time per authorized nonimmigrant validity period. DHS believes that limiting this grace period to one instance during each authorized validity period balances the interests of nonimmigrant flexibility with the need to prevent abuse of this provision.
This 60-day grace period further supports AC21's goals of providing improved certainty and stability to nonimmigrants who need to change jobs or employers. The 60-day grace period would provide needed flexibility to qualifying nonimmigrants who face termination of employment prior to the end of their petition validity periods. The grace period, for example, allows such nonimmigrants to remain in the United States without violating their status and potentially obtain new job offers from employers that seek to file new nonimmigrant petitions, and requests for an extension of stay, on their behalf. In such cases, even though prior employment may have terminated several weeks prior to the filing of the new petition, DHS may consider such an individual to have not violated his or her nonimmigrant status and allow that individual to extend his or her stay with a new petitioner, if otherwise eligible. If the new petition is granted, the individual may be eligible for an additional grace period of up to 60 days in connection with the new authorized validity period."
Finally, the final rule at 8 CFR 214.1(l)(3) makes clear that the nonimmigrant worker, during either a 10-day or 60-day grace period, may apply for and, if otherwise eligible, be granted an extension of stay or change of status. The beneficiary may also commence employment under H-1B portability per § 214.2(h)(2)(i)(H), discussed in some detail below, if otherwise eligible. To further effectuate the intended purpose of these provisions, DHS is also making clarifying edits to the regulatory text at § 214.1(l)(2), and (l)(3)."
Reference: It's in a Federal Register Document (Citation: 81 FR 82398), under Section G "Nonimmigrant Grace Periods", linked here: https://www.federalregister.gov/d/2016-27540/p-553
The document above states: "This final rule is effective January 17, 2017".