diff --git a/contrib/completion/git-completion.bash b/contrib/completion/git-completion.bash
index 56480371ff..e520dda35e 100644
--- a/contrib/completion/git-completion.bash
+++ b/contrib/completion/git-completion.bash
@@ -624,6 +624,19 @@ __git_heads ()
 			"refs/heads/$cur_*" "refs/heads/$cur_*/**"
 }
 
+# Lists branches from remote repositories.
+# 1: A prefix to be added to each listed branch (optional).
+# 2: List only branches matching this word (optional; list all branches if
+#    unset or empty).
+# 3: A suffix to be appended to each listed branch (optional).
+__git_remote_heads ()
+{
+	local pfx="${1-}" cur_="${2-}" sfx="${3-}"
+
+	__git for-each-ref --format="${pfx//\%/%%}%(refname:strip=2)$sfx" \
+			"refs/remotes/$cur_*" "refs/remotes/$cur_*/**"
+}
+
 # Lists tags from the local repository.
 # Accepts the same positional parameters as __git_heads() above.
 __git_tags ()
@@ -783,8 +796,9 @@ __git_refs ()
 # --sfx=<suffix>: A suffix to be appended to each ref instead of the default
 #                 space.
 # --mode=<mode>: What set of refs to complete, one of 'refs' (the default) to
-#                complete all refs, 'heads' to complete only branches. Note
-#                that --remote is only compatible with --mode=refs.
+#                complete all refs, 'heads' to complete only branches, or
+#                'remote-heads' to complete only remote branches. Note that
+#                --remote is only compatible with --mode=refs.
 __git_complete_refs ()
 {
 	local remote dwim pfx cur_="$cur" sfx=" " mode="refs"
@@ -810,6 +824,8 @@ __git_complete_refs ()
 			__gitcomp_direct "$(__git_refs "$remote" "" "$pfx" "$cur_" "$sfx")" ;;
 		heads)
 			__gitcomp_direct "$(__git_heads "$pfx" "$cur_" "$sfx")" ;;
+		remote-heads)
+			__gitcomp_direct "$(__git_remote_heads "$pfx" "$cur_" "$sfx")" ;;
 		*)
 			return 1 ;;
 	esac
@@ -1492,6 +1508,8 @@ _git_checkout ()
 
 		if [ -n "$(__git_find_on_cmdline "-d --detach")" ]; then
 			__git_complete_refs --mode="refs"
+		elif [ -n "$(__git_find_on_cmdline "--track")" ]; then
+			__git_complete_refs --mode="remote-heads"
 		else
 			__git_complete_refs $dwim_opt --mode="refs"
 		fi
@@ -2346,6 +2364,8 @@ _git_switch ()
 
 		if [ -n "$(__git_find_on_cmdline "-d --detach")" ]; then
 			__git_complete_refs --mode="refs"
+		elif [ -n "$(__git_find_on_cmdline "--track")" ]; then
+			__git_complete_refs --mode="remote-heads"
 		else
 			__git_complete_refs $dwim_opt --mode="heads"
 		fi
diff --git a/t/t9902-completion.sh b/t/t9902-completion.sh
index 25d530a8b9..2277326889 100755
--- a/t/t9902-completion.sh
+++ b/t/t9902-completion.sh
@@ -1404,16 +1404,14 @@ test_expect_success 'git checkout - with -d, complete only references' '
 	EOF
 '
 
-#TODO: --track should only complete fully specified remote branches
-test_expect_failure 'git switch - with --track, complete only remote branches' '
+test_expect_success 'git switch - with --track, complete only remote branches' '
 	test_completion "git switch --track " <<-\EOF
 	other/branch-in-other Z
 	other/master-in-other Z
 	EOF
 '
 
-#TODO: --track should only complete fully specified remote branches
-test_expect_failure 'git checkout - with --track, complete only remote branches' '
+test_expect_success 'git checkout - with --track, complete only remote branches' '
 	test_completion "git checkout --track " <<-\EOF
 	other/branch-in-other Z
 	other/master-in-other Z