How do I add tracking number to current order shipment in Magento 2?

AFAIK the track object is the same in M2.

However, the rest of the code has changed.

$data = array(
    'carrier_code' => 'ups',
    'title' => 'United Parcel Service',
    'number' => 'TORD23254WERZXd3', // Replace with your tracking number
);

$track = $this->trackFactory->create()->addData($data);
$shipment->addTrack($track)->save();

Where $this->trackFactory an instance of Magento\Sales\Model\Order\Shipment\TrackFactory and $shipment is your shipment object.

Adding to the accepted answer, it would be a good idea to use repositories instead of the deprecated save method. Also added the customer notification after the tracking creation.

/** @var Magento\Sales\Model\Order\ShipmentRepository */
protected $_shipmentRepository;

/** @var Magento\Shipping\Model\ShipmentNotifier */
protected $_shipmentNotifier;

/** @var Magento\Sales\Model\Order\Shipment\TrackFactory */
protected $_trackFactory; //missing ;

public function __construct(
  \Magento\Shipping\Model\ShipmentNotifier $shipmentNotifier, 
  \Magento\Sales\Model\Order\ShipmentRepository $shipmentRepository, 
  \Magento\Sales\Model\Order\Shipment\TrackFactory $trackFactory)
{
  $this->_shipmentNotifier = $shipmentNotifier;
  $this->_shipmentRepository = $shipmentRepository;
  $this->_trackFactory = $trackFactory;
}
public function addTrack($shipment, $carrierCode, $description, $trackingNumber) 
{
    /** Creating Tracking */
    /** @var Track $track */
    $track = $this->_trackFactory->create();
    $track->setCarrierCode($carrierCode);
    $track->setDescription($description);
    $track->setTrackNumber($trackingNumber);
    $shipment->addTrack($track);
    $this->_shipmentRepository->save($shipment);

    /* Notify the customer*/
    $this->_shipmentNotifier->notify($shipment);
 }

Where $shipment is your shipment object. Notify will notify (send email) to the user and add a history item to the order status history collection.