Output an array of terms for a ‘tax_query’ => array()

I’m trying to use custom fields on the backend to set the taxonomies in a WP_Query for a category archive on the front end.

In the page template. this gets my categories from the custom field:

$terms = get_field('add_categories_custom_template', $term->term_id);

if( $terms ):
foreach( $terms as $term ): 

echo $term; echo ',';

endforeach; 
endif; 

That gives me an output like this:

12,345,900,

But how do I get that output into the 'terms' => array for the tax_query? What I need is the array of IDs to be output this way:

'tax_query' => array(
        array(
            'taxonomy'  => 'product_cat',
            'field'     => 'term_id',
            'terms'     => array('12,345,900'),  // output this way
            'operator'  => 'IN',
        )
   )

But doing this

$terms = get_field('add_categories_custom_template', $term->term_id);

if( $terms ):
foreach( $terms as $term ): 

$my_terms = $term; echo ',';

endforeach; 
endif; 

and this

'tax_query' => array(
        array(
            'taxonomy'  => 'product_cat',
            'field'     => 'term_id',
            'terms' => array($my_terms),
            'operator'  => 'IN',
        )
   )

only outputs the first $term (i.e., 12) and not the subsequent terms (345 and 900).