diff --git a/lisp/minibuffer.el b/lisp/minibuffer.el
index 2120e31775e..2601e705aa0 100644
--- a/lisp/minibuffer.el
+++ b/lisp/minibuffer.el
@@ -2707,8 +2716,14 @@ completion-in-region-mode
 	  completion-in-region-mode-predicate)
     (setq-local minibuffer-completion-auto-choose nil)
     (add-hook 'post-command-hook #'completion-in-region--postch)
-    (push `(completion-in-region-mode . ,completion-in-region-mode-map)
-          minor-mode-overriding-map-alist)))
+    (let* ((keymap completion-in-region-mode-map)
+           (keymap (if minibuffer-completion-visible
+                       (make-composed-keymap
+                        (list minibuffer-local-visible-completion-map
+                              keymap))
+                     keymap)))
+      (push `(completion-in-region-mode . ,keymap)
+            minor-mode-overriding-map-alist))))
 
 ;; Define-minor-mode added our keymap to minor-mode-map-alist, but we want it
 ;; on minor-mode-overriding-map-alist instead.
@@ -2953,7 +2972,32 @@ minibuffer-mode
   :interactive nil
   ;; Enable text conversion, but always make sure `RET' does
   ;; something.
-  (setq text-conversion-style 'action))
+  (setq text-conversion-style 'action)
+  (when minibuffer-completion-visible
+    (setq-local minibuffer-completion-auto-choose nil)))
+
+(defcustom minibuffer-completion-visible t
+  "Non-nil means to navigate completions with arrows from the minibuffer.
+This has effect only when the window with the *Completions* buffer
+is visible on the screen."
+  :type 'boolean
+  :version "30.1")
+
+(defun minibuffer-bind-visible (binding)
+  `(menu-item
+    "" ,binding
+    :filter ,(lambda (cmd)
+               (when (get-buffer-window "*Completions*" 0)
+                 cmd))))
+
+(defvar-keymap minibuffer-local-visible-completion-map
+  :doc "Local keymap for minibuffer input with visible completions."
+  "<left>"  (minibuffer-bind-visible #'minibuffer-previous-completion)
+  "<right>" (minibuffer-bind-visible #'minibuffer-next-completion)
+  "<up>"    (minibuffer-bind-visible #'minibuffer-previous-line-completion)
+  "<down>"  (minibuffer-bind-visible #'minibuffer-next-line-completion)
+  "RET"     (minibuffer-bind-visible #'minibuffer-choose-completion)
+  "C-g"     (minibuffer-bind-visible #'minibuffer-hide-completions))
 
 ;;; Completion tables.
 
@@ -4370,6 +4414,11 @@ completing-read-default
                     ;; in minibuffer-local-filename-completion-map can
                     ;; override bindings in base-keymap.
                     base-keymap)))
+         (keymap (if minibuffer-completion-visible
+                     (make-composed-keymap
+                      (list minibuffer-local-visible-completion-map
+                            keymap))
+                   keymap))
          (buffer (current-buffer))
          (c-i-c completion-ignore-case)
          (result
@@ -4489,8 +4538,9 @@ minibuffer-completion-auto-choose
   :type 'boolean
   :version "29.1")
 
-(defun minibuffer-next-completion (&optional n)
+(defun minibuffer-next-completion (&optional n vertical)
   "Move to the next item in its completions window from the minibuffer.
+When the optional argument VERTICAL is non-nil, move vertically.
 When `minibuffer-completion-auto-choose' is non-nil, then also
 insert the selected completion to the minibuffer."
   (interactive "p")
@@ -4498,7 +4548,9 @@ minibuffer-next-completion
     (with-minibuffer-completions-window
       (when completions-highlight-face
         (setq-local cursor-face-highlight-nonselected-window t))
-      (next-completion (or n 1))
+      (if vertical
+          (next-line-completion (or n 1))
+        (next-completion (or n 1)))
       (when auto-choose
         (let ((completion-use-base-affixes t))
           (choose-completion nil t t))))))
@@ -4510,6 +4562,20 @@ minibuffer-previous-completion
   (interactive "p")
   (minibuffer-next-completion (- (or n 1))))
 
+(defun minibuffer-next-line-completion (&optional n)
+  "Move to the next completion line from the minibuffer.
+When `minibuffer-completion-auto-choose' is non-nil, then also
+insert the selected completion to the minibuffer."
+  (interactive "p")
+  (minibuffer-next-completion (or n 1) t))
+
+(defun minibuffer-previous-line-completion (&optional n)
+  "Move to the previous completion line from the minibuffer.
+When `minibuffer-completion-auto-choose' is non-nil, then also
+insert the selected completion to the minibuffer."
+  (interactive "p")
+  (minibuffer-next-completion (- (or n 1)) t))
+
 (defun minibuffer-choose-completion (&optional no-exit no-quit)
   "Run `choose-completion' from the minibuffer in its completions window.
 With prefix argument NO-EXIT, insert the completion at point to the