Add the Google Tag Manager snippets to a WordPress theme's `functions.php` file.

gtm-add-to-theme.php

<?php
/**
 * Add the Google tag manager script in the header.
 *
 * @since 1.0.0
 *
 */
function prefix_add_google_tag_manager_script() {
	if ( function_exists( 'wp_get_environment_type' )
		&& 'production' !== wp_get_environment_type() ) {
		?>
			<!-- Google Tag Manager: Not loaded on dev environment. -->
		<?php
		return;
	}
	?>
	<!-- Google Tag Manager -->
	<script>(function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':
	new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],
	j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src=
	'https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);
	})(window,document,'script','dataLayer','{GTM_CONTAINER_ID}');</script>
	<!-- End Google Tag Manager -->
	<?php
	// Add the action that creates the noscript version.
	add_action( 'wp_body_open', 'prefix_add_google_tag_manager_noscript_tag' );
}
add_action( 'wp_head', 'prefix_add_google_tag_manager_script' );

/**
 * Add the Google "noscript" tag immediately after the opening of the body element.
 *
 * @since 1.0.0
 *
 */
function prefix_add_google_tag_manager_noscript_tag() {
	?>
	<!-- Google Tag Manager (noscript) -->
	<noscript><iframe src="https://www.googletagmanager.com/ns.html?id={GTM_CONTAINER_ID}"
	height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>
	<!-- End Google Tag Manager (noscript) -->
	<?php
}