diff --git a/llvm/CMakeLists.txt b/llvm/CMakeLists.txt
--- a/llvm/CMakeLists.txt
+++ b/llvm/CMakeLists.txt
@@ -964,12 +964,12 @@
   endif()
 endforeach()
 
-add_subdirectory(projects)
-
 if( LLVM_INCLUDE_TOOLS )
   add_subdirectory(tools)
 endif()
 
+add_subdirectory(projects)
+
 if( LLVM_INCLUDE_RUNTIMES )
   add_subdirectory(runtimes)
 endif()
diff --git a/openmp/README.rst b/openmp/README.rst
--- a/openmp/README.rst
+++ b/openmp/README.rst
@@ -263,14 +263,18 @@
 **LIBOMPTARGET_NVPTX_CUDA_COMPILER** = ``""``
   Location of a CUDA compiler capable of emitting LLVM bitcode. Currently only
   the Clang compiler is supported. This is only used when building the CUDA LLVM
-  bitcode offloading device RTL. If unspecified and the CMake C compiler is
-  Clang, then Clang is used.
+  bitcode offloading device RTL. If unspecified, either the Clang from the build
+  itself is used (i.e. an in-tree build with LLVM_ENABLE_PROJECTS including
+  clang), or the Clang compiler that the build uses as C compiler
+  (CMAKE_C_COMPILER; only if it is Clang). The latter is common for a
+  stage2-build or when using -DLLVM_ENABLE_RUNTIMES=openmp.
 
 **LIBOMPTARGET_NVPTX_BC_LINKER** = ``""``
   Location of a linker capable of linking LLVM bitcode objects. This is only
-  used when building the CUDA LLVM bitcode offloading device RTL. If unspecified
-  and the CMake C compiler is Clang and there exists a llvm-link binary in the
-  directory containing Clang, then this llvm-link binary is used.
+  used when building the CUDA LLVM bitcode offloading device RTL. If
+  unspecified, either the llvm-link in that same directory as
+  LIBOMPTARGET_NVPTX_CUDA_COMPILER is used, or the llvm-link from the
+  same build (available in an in-tree build).
 
 **LIBOMPTARGET_NVPTX_ALTERNATE_HOST_COMPILER** = ``""``
   Host compiler to use with NVCC. This compiler is not going to be used to
diff --git a/openmp/libomptarget/deviceRTLs/nvptx/CMakeLists.txt b/openmp/libomptarget/deviceRTLs/nvptx/CMakeLists.txt
--- a/openmp/libomptarget/deviceRTLs/nvptx/CMakeLists.txt
+++ b/openmp/libomptarget/deviceRTLs/nvptx/CMakeLists.txt
@@ -30,7 +30,17 @@
 
 if (NOT LIBOMPTARGET_NVPTX_CUDA_COMPILER STREQUAL "")
   set(cuda_compiler ${LIBOMPTARGET_NVPTX_CUDA_COMPILER})
+elseif (TARGET clang) # Or query LLVM_TOOL_CLANG_BUILD
+  # Compile the deviceRTL with the clang that is built in the project.
+  set(cuda_compiler clang)
 elseif(${CMAKE_C_COMPILER_ID} STREQUAL "Clang")
+  # Compile the device runtime with the compiler that OpenMP is built with.
+  # This is the case with LLVM_ENABLE_RUNTIMES=openmp.
+  # FIXME: This is unreliable; the compiler can be on older version of clang
+  # that does not support compiling CUDA, or only an older version of it. The
+  # risk is espicially high on sustems where clang is the default compiler
+  # (MacOS, BSDs). LLVM_ENABLE_RUNTIMES=openmp should itself set
+  # LIBOMPTARGET_NVPTX_CUDA_COMPILER instead.
   set(cuda_compiler ${CMAKE_C_COMPILER})
 else()
   libomptarget_say("Not building NVPTX deviceRTL: clang not found")
@@ -44,7 +54,12 @@
 if (NOT LIBOMPTARGET_NVPTX_BC_LINKER STREQUAL "")
   set(bc_linker ${LIBOMPTARGET_NVPTX_BC_LINKER})
 elseif (EXISTS ${llvm_link})
+  # Try to use the linker consistent with the CUDA compiler unless explicitly
+  # set to a different linker.
   set(bc_linker ${llvm_link})
+elseif (TARGET llvm-link)
+  # Use the linker also built in the same project.
+  set(bc_linker llvm-link)
 else()
   libomptarget_say("Not building NVPTX deviceRTL: llvm-link not found")
   return()