How do you change Background for a Button MouseOver in WPF?

I have a button on my page with this XAML:

<Button Content="Button" HorizontalAlignment="Left" VerticalAlignment="Bottom" 
    Width="50" Height="50" HorizontalContentAlignment="Left" 
    BorderBrush="{x:Null}" Foreground="{x:Null}" Margin="50,0,0,0">
    <Button.Style>
        <Style TargetType="Button">
            <Setter Property="Background" Value="Green"/>
            <Style.Triggers>
                <Trigger Property="IsMouseOver" Value="True">
                    <Setter Property="Background" Value="Red"/>
                </Trigger>
            </Style.Triggers>
        </Style>
    </Button.Style>
</Button>

When I put the mouse cursor over my button, the button's background changes to default windows gray background. What's the problem?

This is the button picture before and after mouseover:
Before:

After:

To remove the default MouseOver behaviour on the Button you will need to modify the ControlTemplate. Changing your Style definition to the following should do the trick:

<Style TargetType="{x:Type Button}">
    <Setter Property="Background" Value="Green"/>
    <Setter Property="Template">
        <Setter.Value>
            <ControlTemplate TargetType="{x:Type Button}">
                <Border Background="{TemplateBinding Background}" BorderBrush="Black" BorderThickness="1">
                    <ContentPresenter HorizontalAlignment="Center" VerticalAlignment="Center"/>
                </Border>
            </ControlTemplate>
        </Setter.Value>
    </Setter>
    <Style.Triggers>
        <Trigger Property="IsMouseOver" Value="True">
            <Setter Property="Background" Value="Red"/>
        </Trigger>
    </Style.Triggers>
</Style>

EDIT: It's a few years late, but you are actually able to set the border brush inside of the border that is in there. Idk if that was pointed out but it doesn't seem like it was...