Place Order button in Checkout

This question has been answered here.

Basically, you want to use a switch statement hooked to the gettext filter. One benefit of this method is, if you need to change more text down the line you can just add another case to the function. For example:

add_filter( 'gettext', 'wpsx_replace_text_string', 20, 3 );
function wpsx_replace_text_string( $translated_text, $text, $domain ) {

  if ($domain === 'woocommerce') {
    switch ( $translated_text ) {
        //Text to replace
        case 'Place Order' :
            $translated_text = __( 'Complete Checkout', 'woocommerce' );
            break;
        //More text to replace
        case 'Related Products' :
            $translated_text = __( 'Other Options', 'woocommerce' );
            break;
    } 
  }

  return $translated_text;
}