After hours of searching and testing finally got it just after posting the question!
You can use the "AnchorPane.topAnchor, AnchorPane.bottomAnchor, AnchorPane.leftAnchor, AnchorPane.rightAnchor" fxml commands with the value "0.0" to fit/stretch/align the child elements inside a AnchorPane. So, these commands tell to child element to follow its parent while resizing.
My updated code Main.fxml
<?xml version="1.0" encoding="UTF-8"?>
<?import java.lang.*?>
<?import java.util.*?>
<?import javafx.scene.*?>
<?import javafx.scene.control.*?>
<?import javafx.scene.layout.*?>
<AnchorPane fx:id="anchorPane" xmlns:fx="http://javafx.com/fxml" fx:controller="app.MainController">
<!--<StackPane fx:id="stackPane" ></StackPane>--> <!-- replace with the following -->
<StackPane fx:id="stackPane" AnchorPane.topAnchor="0.0" AnchorPane.bottomAnchor="0.0" AnchorPane.leftAnchor="0.0" AnchorPane.rightAnchor="0.0" ></StackPane>
</AnchorPane>
Here is the result:
For api documentation: http://docs.oracle.com/javafx/2/api/javafx/scene/layout/AnchorPane.html