For the US, this is part of AC 90-108 "Use of Suitable Area Navigation (RNAV) Systems on Conventional Routes and Procedures"
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.
Note GNSS in lieu of DME doesn't include approaches, like ILS/DME. In these approaches the DME may be located at any suitable place, e.g. at the mid point of the runway length, and its 50 µs response delay recalibrated to indicate 0 at the threshold of the active runway. Something the GNSS cannot handle without additional information.