diff --git a/README.md b/README.md
index d5fdb3a0ae..cc40f161cd 100644
--- a/README.md
+++ b/README.md
@@ -140,3 +140,23 @@ verify that it's content is up-to-date.
 The `vendor` directory is optional. It is still present in projects
 because it avoids downloading sources during CI builds. If this is no
 longer deemed necessary, then a project can also remove the directory.
+
+When using packages that are part of the Kubernetes source code, the
+commands above are not enough because the [lack of semantic
+versioning](https://github.com/kubernetes/kubernetes/issues/72638)
+prevents `go mod` from finding newer releases. Importing directly from
+`kubernetes/kubernetes` also needs `replace` statements to override
+the fake `v0.0.0` versions
+(https://github.com/kubernetes/kubernetes/issues/79384). The
+`go-get-kubernetes.sh` script can be used to update all packages in
+lockstep to a different Kubernetes version. It takes a single version
+number like "1.16.0".
+
+Conversion of a repository that uses `dep` to `go mod` can be done with:
+
+    GO111MODULE=on go mod init
+    release-tools/go-get-kubernetes.sh <current Kubernetes version from Gopkg.toml>
+    GO111MODULE=on go mod tidy
+    GO111MODULE=on go mod vendor
+    git rm -f Gopkg.toml Gopkg.lock
+    git add go.mod go.sum vendor
diff --git a/go-get-kubernetes.sh b/go-get-kubernetes.sh
new file mode 100755
index 0000000000..8c4e302445
--- /dev/null
+++ b/go-get-kubernetes.sh
@@ -0,0 +1,104 @@
+#!/usr/bin/env bash
+
+# Copyright 2019 The Kubernetes Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#
+# This script can be used while converting a repo from "dep" to "go mod"
+# by calling it after "go mod init" or to update the Kubernetes packages
+# in a repo that has already been converted. Only packages that are
+# part of kubernetes/kubernetes and thus part of a Kubernetes release
+# are modified. Other k8.io packages (like k8s.io/klog, k8s.io/utils)
+# need to be updated separately.
+
+set -o pipefail
+
+cmd=$0
+
+function help () {
+    echo "$cmd <kubernetes version = x.y.z> - update all components from kubernetes/kubernetes to that version"
+}
+
+if [ $# -ne 1 ]; then
+    help
+    exit 1
+fi
+case "$1" in -h|--help|help) help; exit 0;; esac
+
+die () {
+    echo >&2 "$@"
+    exit 1
+}
+
+k8s="$1"
+
+# If the repo imports k8s.io/kubernetes (directly or indirectly), then
+# "go mod" will try to find "v0.0.0" versions because
+# k8s.io/kubernetes has those in it's go.mod file
+# (https://github.com/kubernetes/kubernetes/blob/2bd9643cee5b3b3a5ecbd3af49d09018f0773c77/go.mod#L146-L157).
+# (https://github.com/kubernetes/kubernetes/issues/79384).
+#
+# We need to replicate the replace statements to override those fake
+# versions also in our go.mod file (idea and some code from
+# https://github.com/kubernetes/kubernetes/issues/79384#issuecomment-521493597).
+mods=$( (set -x; curl --silent --show-error --fail "https://raw.githubusercontent.com/kubernetes/kubernetes/v${k8s}/go.mod") |
+          sed -n 's|.*k8s.io/\(.*\) => ./staging/src/k8s.io/.*|k8s.io/\1|p'
+   ) || die "failed to determine Kubernetes staging modules"
+for mod in $mods; do
+    # The presence of a potentially incomplete go.mod file affects this command,
+    # so move elsewhere.
+    modinfo=$(set -x; cd /; env GO111MODULE=on go mod download -json "$mod@kubernetes-${k8s}") ||
+        die "failed to determine version of $mod: $modinfo"
+    v=$(echo "$modinfo" | sed -n 's|.*"Version": "\(.*\)".*|\1|p')
+    (set -x; env GO111MODULE=on go mod edit "-replace=$mod=$mod@$v") || die "'go mod edit' failed"
+done
+
+packages=
+
+# Beware that we have to work with packages, not modules (i.e. no -m
+# flag), because some modules trigger a "no Go code except tests"
+# error.  Getting their packages works.
+if ! packages=$( (set -x; env GO111MODULE=on go list all) | grep ^k8s.io/ | sed -e 's; *;;'); then
+    cat >&2 <<EOF
+
+Warning: "GO111MODULE=on go list all" failed, trying individual packages instead.
+
+EOF
+    if ! packages=$( (set -x; env GO111MODULE=on go list -f '{{ join .Deps "\n" }}' ./...) | grep ^k8s.io/); then
+        cat >&2 <<EOF
+
+ERROR: could not obtain package list, both of these commands failed:
+       GO111MODULE=on go list all
+       GO111MODULE=on go list -f '{{ join .Deps "\n" }}' ./pkg/...
+EOF
+        exit 1
+    fi
+fi
+
+deps=
+for package in $packages; do
+    # Some k8s.io packages do not come from Kubernetes staging and
+    # thus have different versioning (or none at all...). We need to
+    # skip those.  We know what packages are from staging because we
+    # now have "replace" statements for them in go.mod.
+    #
+    # shellcheck disable=SC2001
+    module=$(echo "$package" | sed -e 's;k8s.io/\([^/]*\)/.*;k8s.io/\1;')
+    if grep -q -w "$module *=>" go.mod; then
+        deps="$deps $(echo "$package" | sed -e "s;\$;@kubernetes-$k8s;" -e 's;^k8s.io/kubernetes\(/.*\)@kubernetes-;k8s.io/kubernetes\1@v;')"
+    fi
+done
+
+# shellcheck disable=SC2086
+(set -x; env GO111MODULE=on go get $deps 2>&1) || die "go get failed"
+echo "SUCCESS"