call a function in success of datatable ajax call

You can use dataSrc :

Here is a typical example of datatables.net

var table = $('#example').DataTable({
    "ajax": {
            "type" : "GET",
            "url" : "ajax.php",
            "dataSrc": function ( json ) {
                //Make your callback here.
                alert("Done!");
                return json.data;
            }       
    },
    "columns": [
            { "data": "name" },
            { "data": "position" },
            { "data": "office" },
            { "data": "extn" },
            { "data": "start_date" },
            { "data": "salary" }
        
        ]
    } );