gistfile1.php

<?php

/**
 * Autocomplete orders with virtual products (WC 2.2+)
 */

add_filter( 'woocommerce_payment_complete_order_status', 'bryce_autocomplete_virtual_orders', 10, 2 );
function bryce_autocomplete_virtual_orders( $order_status, $order_id ) {
	
	$order = wc_get_order( $order_id );

	if ('processing' == $order_status && ('on-hold' == $order->status || 'pending' == $order->status || 'failed' == $order->status)) {
	
		$virtual_order = '';
		if ( count( $order->get_items() ) > 0 ) {
			foreach ( $order->get_items() as $item ) {
				if ( 'line_item' == $item['type'] ) {
					$_product = $order->get_product_from_item( $item );
					if ( ! $_product->is_virtual() ) {
						$virtual_order = false;
						break;
					} else {
						$virtual_order = true;
					}
				}
			}
		}
		if ( $virtual_order ) {
			return 'completed';
		}
	}

	return $order_status;

}

I wasn't able to get this gist working in wooCommerce 2.5.5, but I found a way that works, based on the code above and the code on this page https://docs.woothemes.com/document/automatically-complete-orders/

However, I have only tested this with virtual products, so I don't know how it will affect non virtual products.

/**
 * Tested with wooCommerce 2.5.5
 */

add_filter( 'woocommerce_thankyou', 'bryce_autocomplete_virtual_orders' );
function bryce_autocomplete_virtual_orders( $order_id ) {

    $order = wc_get_order( $order_id );
    if( 'processing' == $order->status ) {
        $virtual_order = '';
        if ( count( $order->get_items() ) > 0 ) {
            foreach ( $order->get_items() as $item ) {
                if ( 'line_item' == $item['type'] ) {
                    $_product = $order->get_product_from_item( $item );
                    if ( ! $_product->is_virtual() ) {
                        $virtual_order = false;
                        break;
                    } else {
                        $virtual_order = true;
                    }
                }
            }
        }
        if ( $virtual_order ) {
            $order->update_status( 'completed' );
        }
    }
}