Edit in JSFiddle

var meses = ["Ene", "Feb", "Mar", "Abr", "May", "Jun", "Jul", "Ago", "Sep", "Oct", "Nov", "Dic"];

$("#fecha").datepicker({
    onClose: function(date){
        var picker = date.split("/"),
            fecha = $("input[name=fecha]"),
            day, month, year;
        
        $(".day.active").html(picker[1]);
        $(".month.active").html(meses[picker[0]-1]);
        $(".year.active").html(picker[2]);
          
        day = $(".day.active").html() + "/";
        month = $(".month.active").html() + "/";
        year = $(".year.active").html();
        
        fecha.val(day + month + year);        
    }
});

<div id="datepicker">
    <div>
        <span class="day">3</span>
        <span class="day active">4</span>
        <span class="day">5</span>
    </div>

    <div>
        <span class="month">May</span>
        <span class="month active">Jun</span>
        <span class="month">Jul</span>
    </div>
        
    <div>
        <span class="year">2013</span>
        <span class="year active">2014</span>
        <span class="year">2015</span>
    </div>
</div>
<input type="text" id="fecha" placeholder="Elige una fecha" />
<input type="text" name="fecha" readOnly>