Using this add-on http://devot-ee.com/add-ons/yearlist you could do this:
Setup your dropdown like so:
<form name="yourform" action="">
<select id="yourselect" name="yourselect">
{exp:yearlist channel="yourchannel"}
<option value="{path=archive}/{year}">{year}</option>
{/exp:yearlist}
</select>
</form>
On your landing page you'd do something like this to display your entries based on year:
{exp:channel:entries channel="news" year="{segment_2}"}
<h1>{title}</h1>
{body}
{/exp:channel:entries}
And use some jQuery to redirect to your year pages:
<script type="text/javascript">
$('#yourselect').change(function() {
window.location = $(this).val();
});
</script>
If you'd like to do it via javascript instead of jQuery checkout this article