diff --git a/libc/CMakeLists.txt b/libc/CMakeLists.txt
--- a/libc/CMakeLists.txt
+++ b/libc/CMakeLists.txt
@@ -146,9 +146,14 @@
 set(LIBC_INSTALL_DEPENDS)
 set(LIBC_INSTALL_TARGET)
 if(LLVM_LIBC_FULL_BUILD)
+  add_llvm_install_targets(
+    install-libc-headers
+    DEPENDS libc-headers
+    COMPONENT libc-headers
+  )
   set(LIBC_TARGET libc)
   set(LIBC_COMPONENT libc)
-  set(LIBC_INSTALL_DEPENDS "libc;libc-headers;libc-startup")
+  set(LIBC_INSTALL_DEPENDS "libc;install-libc-headers;libc-startup")
   set(LIBC_INSTALL_TARGET install-libc)
   set(LIBC_ARCHIVE_NAME c)
 else()
diff --git a/libc/include/CMakeLists.txt b/libc/include/CMakeLists.txt
--- a/libc/include/CMakeLists.txt
+++ b/libc/include/CMakeLists.txt
@@ -266,5 +266,5 @@
   get_filename_component(nested_dir ${relative_path} DIRECTORY)
   install(FILES ${header_file}
           DESTINATION ${CMAKE_INSTALL_INCLUDEDIR}/${nested_dir}
-          COMPONENT ${LIBC_COMPONENT})
+          COMPONENT libc-headers)
 endforeach()