function callback(data) {
    return data;
}

var xv = jQuery.ajax( {
    url: 'http://www.domain.com/json.php',
    dataType: 'json',
    success: function(data) {
        alert('Success.'); // This is alerted.
    },
    error: function(data) {
        alert('File could not be processed.'); // This is not alerted.
    },
    complete: function(data) {
        callback(data);
    }
});

console.log(callback()); // Getting "undefined" here instead of data.