diff --git a/G/Gloo/build_tarballs.jl b/G/Gloo/build_tarballs.jl
index dd2ebd5ad18..5ca9f760f58 100644
--- a/G/Gloo/build_tarballs.jl
+++ b/G/Gloo/build_tarballs.jl
@@ -15,12 +15,16 @@ script = raw"""
 cd $WORKSPACE/srcdir/gloo
 mkdir build
 cd build
+if [[ $bb_full_target == *cuda* ]]; then
+    cmake_extra_args="-DUSE_CUDA=ON -DCUDA_TOOLKIT_ROOT_DIR=$prefix/cuda"
+fi
 cmake \
     -DCMAKE_INSTALL_PREFIX=$prefix \
     -DCMAKE_TOOLCHAIN_FILE=${CMAKE_TARGET_TOOLCHAIN} \
     -DCMAKE_BUILD_TYPE=Release \
     -DBUILD_SHARED_LIBS=ON \
     -DUSE_LIBUV=ON \
+    $cmake_extra_args \
     ..
 cmake --build . -- -j $nproc
 make install
@@ -31,7 +35,14 @@ make install
 platforms = supported_platforms()
 filter!(p -> nbits(p) == 64, platforms) # Gloo can only be built on 64-bit systems
 filter!(!Sys.iswindows, platforms) # Windows support will be available from 20200910, i.e. 881f7f0dcf06f7e49e134a45d3284860fb244fa9
+cuda_platforms = Platform[]
+for cuda_version in [v"10.2", v"11.0", v"11.1", v"11.2", v"11.3", v"11.4", v"11.5", v"11.6"]
+    cuda_platform = Platform("x86_64", "linux"; cuda = "$(cuda_version.major).$(cuda_version.minor)")
+    push!(platforms, cuda_platform)
+    push!(cuda_platforms, cuda_platform)
+end
 platforms = expand_cxxstring_abis(platforms)
+cuda_platforms = expand_cxxstring_abis(cuda_platforms)
 
 # The products that we will ensure are always built
 products = [
@@ -41,6 +52,7 @@ products = [
 # Dependencies that must be installed before this package can be built
 dependencies = [
     Dependency("LibUV_jll", v"2.0.0"),
+    BuildDependency("CUDA_full_jll"; platforms = cuda_platforms),
 ]
 
 # Build the tarballs, and possibly a `build.jl` as well.