Shell variable issue when trying to mkdir

Any ideas what is wrong with this code?

CLIENT_BUILD_DIR="~/Desktop/TempDir/"

if [ ! -d $CLIENT_BUILD_DIR ]
then
   {
      mkdir $CLIENT_BUILD_DIR
   }
fi

I get the error: mkdir: ~/Desktop: No such file or directory.

Obviously the directory is there and the script works if I replace the variable with ~/Desktop/TempDir/