How to make a floated div 100% height of its parent?

For the parent:

display: flex;

You should add some prefixes http://css-tricks.com/using-flexbox/

Edit: Only drawback is IE as usual, IE9 does not support flex. http://caniuse.com/flexbox

Edit 2: As @toddsby noted, align items is for parent, and its default value actually is stretch. If you want a different value for child, there is align-self property.

Edit 3: jsFiddle: https://jsfiddle.net/bv71tms5/2/

Actually, as long as the parent element is positioned, you can set the child's height to 100%. Namely, in case you don't want the parent to be absolutely positioned. Let me explain further:

<style>
    #outer2 {
        padding-left: 23px;
        position: relative; 
        height:auto; 
        width:200px; 
        border: 1px solid red; 
    }
    #inner2 {
        left:0;
        position:absolute; 
        height:100%; 
        width:20px; 
        border: 1px solid black; 
    }
</style>

<div id='outer2'>
    <div id='inner2'>
    </div>
</div>

For #outer height to be based on its content, and have #inner base its height on that, make both elements absolutely positioned.

More details can be found in the spec for the css height property, but essentially, #inner must ignore #outer height if #outer's height is auto, unless #outer is positioned absolutely. Then #inner height will be 0, unless #inner itself is positioned absolutely.

<style>
    #outer {
        position:absolute; 
        height:auto; width:200px; 
        border: 1px solid red; 
    }
    #inner {
        position:absolute; 
        height:100%; 
        width:20px; 
        border: 1px solid black; 
    }
</style>

<div id='outer'>
    <div id='inner'>
    </div>
    text
</div>

However... By positioning #inner absolutely, a float setting will be ignored, so you will need to choose a width for #inner explicitly, and add padding in #outer to fake the text wrapping I suspect you want. For example, below, the padding of #outer is the width of #inner +3. Conveniently (as the whole point was to get #inner height to 100%) there's no need to wrap text beneath #inner, so this will look just like #inner is floated.

<style>
    #outer2{
        padding-left: 23px;
        position:absolute; 
        height:auto; 
        width:200px; 
        border: 1px solid red; 
    }
    #inner2{
        left:0;
        position:absolute; 
        height:100%; 
        width:20px; 
        border: 1px solid black; 
   }
</style>

<div id='outer2'>
    <div id='inner2'>
    </div>
    text
</div>

I deleted my previous answer, as it was based on too many wrong assumptions about your goal.