diff --git a/libc/CMakeLists.txt b/libc/CMakeLists.txt
--- a/libc/CMakeLists.txt
+++ b/libc/CMakeLists.txt
@@ -141,6 +141,22 @@
   add_subdirectory(utils/HdrGen)
 endif()
 
+set(LIBC_TARGET)
+set(LIBC_COMPONENT)
+set(LIBC_INSTALL_DEPENDS)
+set(LIBC_INSTALL_TARGET)
+if(LLVM_LIBC_FULL_BUILD)
+  set(LIBC_TARGET c)
+  set(LIBC_COMPONENT libc)
+  set(LIBC_INSTALL_DEPENDS "c;libc-headers")
+  set(LIBC_INSTALL_TARGET install-libc)
+else()
+  set(LIBC_TARGET llvmlibc)
+  set(LIBC_COMPONENT llvmlibc)
+  set(LIBC_INSTALL_DEPENDS llvmlibc)
+  set(LIBC_INSTALL_TARGET install-llvmlibc)
+endif()
+
 add_subdirectory(include)
 add_subdirectory(config)
 add_subdirectory(src)
@@ -168,3 +184,9 @@
 if (LIBC_INCLUDE_DOCS)
   add_subdirectory(docs)
 endif()
+
+add_llvm_install_targets(
+  ${LIBC_INSTALL_TARGET}
+  DEPENDS ${LIBC_INSTALL_DEPENDS}
+  COMPONENT ${LIBC_COMPONENT}
+)
diff --git a/libc/cmake/modules/LLVMLibCHeaderRules.cmake b/libc/cmake/modules/LLVMLibCHeaderRules.cmake
--- a/libc/cmake/modules/LLVMLibCHeaderRules.cmake
+++ b/libc/cmake/modules/LLVMLibCHeaderRules.cmake
@@ -35,10 +35,25 @@
 
   if(ADD_HEADER_DEPENDS)
     get_fq_deps_list(fq_deps_list ${ADD_HEADER_DEPENDS})
+    # Dependencies of a add_header target can only be another add_header target
+    # or an add_gen_header target.
+    foreach(dep IN LISTS fq_deps_list)
+      get_target_property(header_file ${dep} HEADER_FILE_PATH)
+      if(NOT header_file)
+        message(FATAL_ERROR "Invalid dependency '${dep}' for '${fq_target_name}'.")
+      endif()
+    endforeach()
     add_dependencies(
       ${fq_target_name} ${fq_deps_list}
     )
   endif()
+
+  set_target_properties(
+    ${fq_target_name}
+    PROPERTIES
+      HEADER_FILE_PATH ${dest_file}
+      DEPS "${fq_deps_list}"
+  )
 endfunction(add_header)
 
 # A rule for generated header file targets.
@@ -53,7 +68,7 @@
 function(add_gen_header target_name)
   cmake_parse_arguments(
     "ADD_GEN_HDR"
-    "" # No optional arguments
+    "PUBLIC" # No optional arguments
     "DEF_FILE;GEN_HDR" # Single value arguments
     "PARAMS;DATA_FILES;DEPENDS"     # Multi value arguments
     ${ARGN}
@@ -108,9 +123,24 @@
 
   if(ADD_GEN_HDR_DEPENDS)
     get_fq_deps_list(fq_deps_list ${ADD_GEN_HDR_DEPENDS})
+    # Dependencies of a add_header target can only be another add_gen_header target
+    # or an add_header target.
+    foreach(dep IN LISTS fq_deps_list)
+      get_target_property(header_file ${dep} HEADER_FILE_PATH)
+      if(NOT header_file)
+        message(FATAL_ERROR "Invalid dependency '${dep}' for '${fq_target_name}'.")
+      endif()
+    endforeach()
   endif()
   add_custom_target(
     ${fq_target_name}
     DEPENDS ${out_file} ${fq_deps_list}
   )
+
+  set_target_properties(
+    ${fq_target_name}
+    PROPERTIES
+      HEADER_FILE_PATH ${out_file}
+      DEPS "${fq_deps_list}"
+  )
 endfunction(add_gen_header)
diff --git a/libc/cmake/modules/LLVMLibCRules.cmake b/libc/cmake/modules/LLVMLibCRules.cmake
--- a/libc/cmake/modules/LLVMLibCRules.cmake
+++ b/libc/cmake/modules/LLVMLibCRules.cmake
@@ -1,6 +1,5 @@
 include(LLVMLibCTargetNameUtils)
 include(LLVMLibCFlagRules)
-include(LLVMLibCHeaderRules)
 include(LLVMLibCObjectRules)
 include(LLVMLibCLibraryRules)
 include(LLVMLibCTestRules)
diff --git a/libc/include/CMakeLists.txt b/libc/include/CMakeLists.txt
--- a/libc/include/CMakeLists.txt
+++ b/libc/include/CMakeLists.txt
@@ -1,3 +1,6 @@
+set(LIBC_INCLUDE_BINARY_DIR ${CMAKE_CURRENT_BINARY_DIR})
+include(LLVMLibCHeaderRules)
+
 add_subdirectory(llvm-libc-macros)
 add_subdirectory(llvm-libc-types)
 
@@ -217,3 +220,39 @@
   DATA_FILES
     ../config/${LIBC_TARGET_OS}/syscall_numbers.h.inc
 )
+
+if(NOT LLVM_LIBC_FULLBUILD)
+  # We don't install headers in non-fullbuild mode.
+  return()
+endif()
+
+function(get_all_install_header_targets out_var)
+  set(all_deps ${ARGN})
+  foreach(target IN LISTS ARGN)
+    get_target_property(deps ${target} DEPS)
+    if(NOT deps)
+      continue()
+    endif()
+    list(APPEND all_deps ${deps})
+    get_all_install_header_targets(nested_deps ${deps})
+    list(APPEND all_deps ${nested_deps})
+  endforeach()
+  list(REMOVE_DUPLICATES all_deps)
+  set(${out_var} ${all_deps} PARENT_SCOPE)
+endfunction(get_all_install_header_targets)
+
+get_all_install_header_targets(all_install_header_targets ${TARGET_PUBLIC_HEADERS})
+add_custom_target(libc-headers)
+add_dependencies(libc-headers ${all_install_header_targets})
+foreach(target IN LISTS all_install_header_targets)
+  get_target_property(header_file ${target} HEADER_FILE_PATH)
+  if(NOT header_file)
+    message(FATAL_ERROR "Installable header file '${target}' does not have the "
+                        "HEADER_FILE_PATH property set.")
+  endif()
+  file(RELATIVE_PATH relative_path ${LIBC_INCLUDE_BINARY_DIR} ${header_file})
+  get_filename_component(nested_dir ${relative_path} DIRECTORY)
+  install(FILES ${header_file}
+          DESTINATION ${CMAKE_INSTALL_INCLUDEDIR}/${nested_dir}
+          COMPONENT ${LIBC_COMPONENT})
+endforeach()
diff --git a/libc/lib/CMakeLists.txt b/libc/lib/CMakeLists.txt
--- a/libc/lib/CMakeLists.txt
+++ b/libc/lib/CMakeLists.txt
@@ -1,5 +1,5 @@
 add_entrypoint_library(
-  llvmlibc
+  ${LIBC_TARGET}
   DEPENDS
   ${TARGET_LLVMLIBC_ENTRYPOINTS}
 )
@@ -11,13 +11,7 @@
 endif()
 
 install(
-  TARGETS llvmlibc
+  TARGETS ${LIBC_TARGET}
   ARCHIVE DESTINATION "${LIBC_INSTALL_LIBRARY_DIR}"
-  COMPONENT llvmlibc
-)
-
-add_llvm_install_targets(
-  install-llvmlibc
-  DEPENDS llvmlibc
-  COMPONENT llvmlibc
+  COMPONENT ${LIBC_COMPONENT}
 )