You can use this following query to get the total number of orders.
$order_totals = apply_filters( 'woocommerce_reports_sales_overview_order_totals', $wpdb->get_row( "
SELECT COUNT(posts.ID) AS total_orders FROM {$wpdb->posts} AS posts
LEFT JOIN {$wpdb->postmeta} AS meta ON posts.ID = meta.post_id
LEFT JOIN {$wpdb->term_relationships} AS rel ON posts.ID=rel.object_ID
LEFT JOIN {$wpdb->term_taxonomy} AS tax USING( term_taxonomy_id )
LEFT JOIN {$wpdb->terms} AS term USING( term_id )
WHERE meta.meta_key = '_order_total'
AND posts.post_type="shop_order"
AND posts.post_status="publish"
AND tax.taxonomy = 'shop_order_status'
AND term.slug IN ('" . implode( "','",
apply_filters( 'woocommerce_reports_order_statuses',
array( 'completed', 'processing', 'on-hold' ) ) ) . "')
" ) );
$total_orders_count = absint( $order_totals->total_orders );