Multiline Textbox with automatic vertical scroll

If you don't like code behind to much, here is an AttachedProperty that will do the trick :

namespace YourProject.YourAttachedProperties
{

    public class TextBoxAttachedProperties
    {

        public static bool GetAutoScrollToEnd(DependencyObject obj)
        {
            return (bool)obj.GetValue(AutoScrollToEndProperty);
        }

        public static void SetAutoScrollToEnd(DependencyObject obj, bool value)
        {
            obj.SetValue(AutoScrollToEndProperty, value);
        }

        // Using a DependencyProperty as the backing store for AutoScrollToEnd.  This enables animation, styling, binding, etc...
        public static readonly DependencyProperty AutoScrollToEndProperty =
        DependencyProperty.RegisterAttached("AutoScrollToEnd", typeof(bool), typeof(TextBoxAttachedProperties), new PropertyMetadata(false, AutoScrollToEndPropertyChanged));

        private static void AutoScrollToEndPropertyChanged(DependencyObject d, DependencyPropertyChangedEventArgs e)
        {
            if(d is TextBox textbox && e.NewValue is bool mustAutoScroll && mustAutoScroll)
            {
                textbox.TextChanged += (s, ee)=> AutoScrollToEnd(s, ee, textbox);
            }
        }

        private static void AutoScrollToEnd(object sender, TextChangedEventArgs e, TextBox textbox)
        {
            textbox.ScrollToEnd();
        }
    }
}

And then in your xaml just do :

<TextBox
    AcceptsReturn="True"
    myAttachedProperties:TextBoxAttachedProperties.AutoScrollToEnd="True"/>

Just don't forget to add at the top of your xaml file

xmlns:myAttachedProperties="clr-namespace:YourProject.YourAttachedProperties"

And voila

If you make it into a simple custom control then you don't need any code behind to do the scrolling.

public class ScrollingTextBox : TextBox {

    protected override void OnInitialized (EventArgs e) {
        base.OnInitialized(e);
        VerticalScrollBarVisibility = ScrollBarVisibility.Auto;
        HorizontalScrollBarVisibility = ScrollBarVisibility.Auto;
    }

    protected override void OnTextChanged (TextChangedEventArgs e) {
        base.OnTextChanged(e);
        CaretIndex = Text.Length;
        ScrollToEnd();
    }

}

If you're using WPF it would be far better to use binding rather than passing the text box around in the code behind.

According to this question: TextBox.ScrollToEnd doesn't work when the TextBox is in a non-active tab

You have to focus the text box, update the caret position and then scroll to end:

Status.Focus();
Status.CaretIndex = Status.Text.Length;
Status.ScrollToEnd();

EDIT

Example TextBox:

<TextBox TextWrapping="Wrap" VerticalScrollBarVisibility="Auto" 
         AcceptsReturn="True" Name="textBox"/>