diff --git a/gnu/packages/tls.scm b/gnu/packages/tls.scm
index a4e754e27f..af91e42888 100644
--- a/gnu/packages/tls.scm
+++ b/gnu/packages/tls.scm
@@ -313,6 +313,31 @@ required structures.")
 (define-public guile3.0-gnutls
   (deprecated-package "guile3.0-gnutls" gnutls))
 
+(define (target->openssl-target target)
+  "Return the value to set CONFIGURE_TARGET_ARCH to when cross-compiling
+OpenSSL for TARGET."
+  ;; Keep this code outside the build code,
+  ;; such that new targets can be added
+  ;; without causing rebuilds for other targets.
+  (cond ((string-prefix? "i586" target)
+         "hurd-x86")
+        ((string-prefix? "i686" target)
+         "linux-x86")
+        ((string-prefix? "x86_64" target)
+         "linux-x86_64")
+        ((string-prefix? "mips64el" target)
+         "linux-mips64")
+        ((string-prefix? "arm" target)
+         "linux-armv4")
+        ((string-prefix? "aarch64" target)
+         "linux-aarch64")
+        ((string-prefix? "powerpc64le" target)
+         "linux-ppc64le")
+        ((string-prefix? "powerpc64" target)
+         "linux-ppc64")
+        ((string-prefix? "powerpc" target)
+         "linux-ppc")))
+
 (define-public openssl
   (package
    (name "openssl")
@@ -351,25 +376,8 @@ required structures.")
                (lambda* (#:key target #:allow-other-keys)
                  (setenv "CROSS_COMPILE" (string-append target "-"))
                  (setenv "CONFIGURE_TARGET_ARCH"
-                         (cond
-                           ((string-prefix? "i586" target)
-                            "hurd-x86")
-                           ((string-prefix? "i686" target)
-                            "linux-x86")
-                           ((string-prefix? "x86_64" target)
-                            "linux-x86_64")
-                           ((string-prefix? "mips64el" target)
-                            "linux-mips64")
-                           ((string-prefix? "arm" target)
-                            "linux-armv4")
-                           ((string-prefix? "aarch64" target)
-                            "linux-aarch64")
-                           ((string-prefix? "powerpc64le" target)
-                            "linux-ppc64le")
-                           ((string-prefix? "powerpc64" target)
-                            "linux-ppc64")
-                           ((string-prefix? "powerpc" target)
-                            "linux-ppc"))))))
+                         #$(target->openssl-target
+                            (%current-target-system))))))
              #~())
         (replace 'configure
           (lambda _