If you are willing to put a container element around your image, a pure CSS solution is simple. You see, 99% height has no meaning when the parent element will extend vertically to contain its children. The parent needs to have a fixed height, say... the height of the viewport.
HTML
<!-- use a tall image to illustrate the problem -->
<div class='fill-screen'>
<img class='make-it-fit'
src='https://upload.wikimedia.org/wikipedia/commons/f/f2/Leaning_Tower_of_Pisa.jpg'>
</div>
CSS
div.fill-screen {
position: fixed;
left: 0;
right: 0;
top: 0;
bottom: 0;
text-align: center;
}
img.make-it-fit {
max-width: 99%;
max-height: 99%;
}
Play with the fiddle.