For the US, this is part of [AC 90-108 "*Use of Suitable Area Navigation (RNAV) Systems on Conventional Routes and Procedures*"][1]

> 7.a: Usage of Suitable RNAV Systems. Subject to the operating requirements in this AC, operators may use a suitable RNAV system in the following ways
>
> (1) Determine aircraft position relative to or distance from a VOR (see first note in subparagraph 7b), TACAN, NDB, compass locator (see second note in subparagraph 7b), DME fix; or a named fix defined by a VOR radial, TACAN course, NDB bearing, or compass locator bearing intersecting a VOR or Localizer (LOC) course.  
(2) Navigate to or from a VOR, TACAN, NDB, or compass locator.  
(3) Hold over a VOR, TACAN, NDB, compass locator, or DME fix.  
(4) Fly an arc based upon DME

Summary on the AOPA site: [Use of GPS in lieu of DME/ADF][2].


  [1]: https://www.faa.gov/documentLibrary/media/Advisory_Circular/AC_90-108_CHG_1.pdf
  [2]: https://www.aopa.org/advocacy/advocacy-briefs/air-traffic-services-brief-use-of-gps-in-lieu-of-dme-adf