How to detect when WIFI Connection has been established in Android?

You can register a BroadcastReceiver to be notified when a WiFi connection is established (or if the connection changed).

Register the BroadcastReceiver:

IntentFilter intentFilter = new IntentFilter();
intentFilter.addAction(WifiManager.SUPPLICANT_CONNECTION_CHANGE_ACTION);
registerReceiver(broadcastReceiver, intentFilter);

And then in your BroadcastReceiver do something like this:

@Override
public void onReceive(Context context, Intent intent) {
    final String action = intent.getAction();
    if (action.equals(WifiManager.SUPPLICANT_CONNECTION_CHANGE_ACTION)) {
        if (intent.getBooleanExtra(WifiManager.EXTRA_SUPPLICANT_CONNECTED, false)) {
            //do stuff
        } else {
            // wifi connection was lost
        }
    }
}

For more info, see the documentation for BroadcastReceiver and WifiManager

Of course you should check whether the device is already connected to WiFi before this.

EDIT:
Thanks to ban-geoengineering, here’s a method to check whether the device is already connected:

private boolean isConnectedViaWifi() {
     ConnectivityManager connectivityManager = (ConnectivityManager) appObj.getSystemService(Context.CONNECTIVITY_SERVICE);
     NetworkInfo mWifi = connectivityManager.getNetworkInfo(ConnectivityManager.TYPE_WIFI);     
     return mWifi.isConnected();
}