functions.php

add_action( 'woocommerce_order_status_completed', 'change_role_on_purchase' );
function change_role_on_purchase( $order_id ) {
    $order = wc_get_order( $order_id );
    $items = $order->get_items();

    $products_to_check = array( '1', '2', '3' );

    foreach ( $items as $item ) {
        if ( $order->user_id > 0 && in_array( $item['product_id'], $products_to_check ) ) {
        	$user = new WP_User( $order->user_id );

        	// Change role
        	$user->remove_role( 'customer' );
        	$user->add_role( 'new-role' );

            // Exit the loop
            break;
    	}
    }
}