How to a add a command to a WPF TextBlock?

You can use a InputBinding.

<TextBlock Text="Hello">
    <TextBlock.InputBindings>
        <MouseBinding Command="" MouseAction="LeftClick" />
    </TextBlock.InputBindings>
</TextBlock>

Edit: Hyperlink is probably worth a mention too.

<TextBlock><Hyperlink Command="" TextDecorations="None" Foreground="Black">Hello</Hyperlink></TextBlock>

You do not make a transparent button over it, you put the TextBlock into it:

<Button>
    <Button.Template>
        <ControlTemplate TargetType="Button">
            <ContentPresenter />
        </ControlTemplate>
    </Button.Template>
    <TextBlock Text="Lorem Ipsum"/>
</Button>