diff --git a/tools/workspace/gfortran/package.BUILD.bazel b/tools/workspace/gfortran/package.BUILD.bazel
new file mode 100644
index 000000000000..342ef50c3f20
--- /dev/null
+++ b/tools/workspace/gfortran/package.BUILD.bazel
@@ -0,0 +1,36 @@
+# -*- bazel -*-
+
+load("@drake//tools/skylark:cc.bzl", "cc_library")
+load(":path.bzl", "LIBDIR")
+
+# libgfortran: GPL-3.0-or-later WITH GCC-exception-3.1.
+# libquadmath: LGPL-2.0-or-later.
+licenses(["restricted"])  # See above for details.
+
+sh_binary(
+    name = "compiler",
+    srcs = ["gfortran-found"],
+    visibility = ["//visibility:public"],
+)
+
+config_setting(
+    name = "x86_64",
+    constraint_values = [
+        "@platforms//cpu:x86_64",
+    ],
+)
+
+cc_library(
+    name = "runtime",
+    linkopts = [
+        "-L{}".format(LIBDIR),
+        "-ldl",
+        "-lgfortran",
+    ] + select({
+        ":x86_64": [
+            "-lquadmath",
+        ],
+        "//conditions:default": [],
+    }),
+    visibility = ["//visibility:public"],
+)
diff --git a/tools/workspace/gfortran/repository.bzl b/tools/workspace/gfortran/repository.bzl
index 20f3b69a3355..bb3354bda938 100644
--- a/tools/workspace/gfortran/repository.bzl
+++ b/tools/workspace/gfortran/repository.bzl
@@ -1,86 +1,46 @@
-load("//tools/workspace:os.bzl", "determine_os")
 load("//tools/workspace:execute.bzl", "execute_or_fail", "which")
 
-def _find_library(repo_ctx, compiler, lib_name):
-    return execute_or_fail(
-        repo_ctx,
-        [compiler, "--print-file-name=" + lib_name],
-    ).stdout.strip()
-
 def _gfortran_impl(repo_ctx):
-    """Locate gfortran and alias it to `:compiler`; locate libgfortran and
-    libquadmath and alias then to `:runtime.`"""
-
     # Find the compiler.
     compiler = str(which(repo_ctx, "gfortran"))
     if not compiler:
         fail("Could not find gfortran")
     repo_ctx.symlink(compiler, "gfortran-found")
 
-    # Find the runtime libraries based on the OS.
-    os_result = determine_os(repo_ctx)
-    if os_result.error != None:
-        fail(os_result.error)
-    if os_result.is_macos or os_result.is_macos_wheel:
-        suffix = ".dylib"
-    else:
-        suffix = ".so"
-    libgfortran = "libgfortran{}".format(suffix)
-    libgfortran_path = _find_library(repo_ctx, compiler, libgfortran)
-
-    # The cc_library linking is different on Ubuntu vs macOS.
-    if os_result.is_macos or os_result.is_macos_wheel:
-        srcs = []
-        linkopts = [
-            "-L{}".format(repo_ctx.path(libgfortran_path).dirname),
-            "-ldl",
-            "-lgfortran",
-        ]
-        if os_result.macos_arch_result != "arm64":
-            linkopts.append("-lquadmath")
-    else:
-        libquadmath = "libquadmath{}".format(suffix)
-        libquadmath_path = _find_library(repo_ctx, compiler, libquadmath)
-        repo_ctx.symlink(libgfortran_path, libgfortran)
-        repo_ctx.symlink(libquadmath_path, libquadmath)
-        srcs = [libgfortran, libquadmath]
-        linkopts = ["-ldl"]
-
-    # Inquire which version we found.
+    # Transcribe which version we found.
     dumpversion = execute_or_fail(repo_ctx, [compiler, "-dumpversion"]).stdout
-    repo_ctx.file("version.bzl", content = "MAJOR = {}\n".format(
-        int(dumpversion.strip()),
-    ))
-
-    # Emit the build file and return.
-    BUILD = """
-    # DO NOT EDIT: generated by gfortran_repository().
-
-    load("@drake//tools/skylark:cc.bzl", "cc_library")
-
-    # libgfortran: GPL-3.0-or-later WITH GCC-exception-3.1.
-    # libquadmath: LGPL-2.0-or-later.
-    licenses(["restricted"])  # See above for details.
-
-    sh_binary(
-        name = "compiler",
-        srcs = ["gfortran-found"],
-        visibility = ["//visibility:public"],
+    repo_ctx.file(
+        "version.bzl",
+        content = "MAJOR = {}\n".format(int(dumpversion.strip())),
     )
-    cc_library(
-        name = "runtime",
-        srcs = {},
-        linkopts = {},
-        visibility = ["//visibility:public"],
+
+    # Transcribe the library link path.
+    filename = execute_or_fail(
+        repo_ctx,
+        [
+            compiler,
+            "--print-file-name=libgfortran.{}".format(
+                "dylib" if repo_ctx.os.name == "mac os x" else "so",
+            ),
+        ],
+    ).stdout
+    libdir = repo_ctx.path(filename.strip()).dirname
+    repo_ctx.file(
+        "path.bzl",
+        content = "LIBDIR = {}\n".format(repr(str(libdir))),
     )
-    """.format(srcs, linkopts).replace(
-        # Strip leading indentation.
-        "\n    ",
-        "\n",
+
+    # Add the build file.
+    repo_ctx.symlink(
+        Label("@drake//tools/workspace/gfortran:package.BUILD.bazel"),
+        "BUILD.bazel",
     )
-    repo_ctx.file("BUILD.bazel", content = BUILD)
 
 gfortran_repository = repository_rule(
+    doc = """
+        Locate gfortran and alias it to `:compiler`; locate libgfortran
+        (and libquadmath when relevant) and alias them to `:runtime`.
+    """,
     local = True,
     configure = True,
     implementation = _gfortran_impl,