How to rebuild ELPA packages after upgrade of Emacs

I just upgraded GNU Emacs from 23 to 24 on MacOS and some ELPA installed packages stopped working. One of them is AucTeX. Deleting it and reinstalling it through the package manager made it work again, but I don't want to do this by hand for every package. I'm slightly confused that I find nothing about that on the Internet.

Don't the .elc need to be recompiled for a new version of Emacs? Why isn't this a feature of package.el?

You do not need to re-install all packages. The packages itself are likely fine, however, they need to be re-compiled, because Emacs Lisp byte code is generally not compatible across major versions.

To re-compile all packages, type M-: (byte-recompile-directory package-user-dir nil 'force). After restarting Emacs, packages should work fine again.

This works for me on Emacs 25.1 and 26:

(defun package-reinstall-all-activated-packages ()
  "Refresh and reinstall all activated packages."
  (interactive)
  (package-refresh-contents)
  (dolist (package-name package-activated-list)
    (when (package-installed-p package-name)
      (unless (ignore-errors                   ;some packages may fail to install
                (package-reinstall package-name))
        (warn "Package %s failed to reinstall" package-name)))))

The variable package-activated-list holds the list of packages we're interested in. So we just need to install each one again. We don't need to explicitly delete them; calling package-install will blow away an old version.

Put this code in a scratch buffer and evaluate it (that is, put your cursor at the end, and press C-x C-e):

(dolist (package-name package-activated-list)
  (package-install package-name))

my recipe after emacs 25:

1. in .emacs (define your packages list):

> (custom-set-variables > '(package-selected-packages > (quote > (browse-kill-ring helm undo-tree use-package)))

2. in a terminal:

> $ rm -rf ~/.emacs.d/elpa/*

3. in emacs:

> (progn (package-refresh-contents) > (package-install-selected-packages) > (byte-recompile-directory package-user-dir nil 'force))