diff --git a/Library/Homebrew/os.rb b/Library/Homebrew/os.rb
index 6dfeeb460f..a22add846f 100644
--- a/Library/Homebrew/os.rb
+++ b/Library/Homebrew/os.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require "version"
@@ -31,7 +31,7 @@ module OS
   sig { returns(Version) }
   def self.kernel_version
     require "utils/popen"
-    @kernel_version ||= Version.new(Utils.safe_popen_read("uname", "-r").chomp)
+    @kernel_version ||= T.let(Version.new(Utils.safe_popen_read("uname", "-r").chomp), T.nilable(Version))
   end
 
   # Get the kernel name.
@@ -40,10 +40,10 @@ module OS
   sig { returns(String) }
   def self.kernel_name
     require "utils/popen"
-    @kernel_name ||= Utils.safe_popen_read("uname", "-s").chomp
+    @kernel_name ||= T.let(Utils.safe_popen_read("uname", "-s").chomp, T.nilable(String))
   end
 
-  ::OS_VERSION = ENV.fetch("HOMEBREW_OS_VERSION").freeze
+  ::OS_VERSION = T.let(ENV.fetch("HOMEBREW_OS_VERSION").freeze, String)
 
   # See Linux-CI.md
   LINUX_CI_OS_VERSION = "Ubuntu 22.04"