WordPress/WooCommerce API Function

I’m adding a function to WordPress to be run when an order has been placed on WooCommerce.

The API call is to add a delivery to the DeTrack System (http://www.detrack.com/api-documentation/add-deliveries/) via their API. This is in the form of a HTTP Post Request.

[
   {
      "date":"2014-02-11",
      "do":"DO140211001",
      "address":"63 Ubi Avenue 1 Singapore 408937",
      "delivery_time":"09:00 AM - 12:00 PM",
      "deliver_to":"John Tan",
      "phone":"+6591234567",
      "notify_email":"john.tan@example.com",
      "notify_url":"http://www.example.com/notify.php",
      "assign_to":"GT1234H",
      "instructions":"Call customer upon arrival.",
      "zone":"East",
      "items":[
         {
            "sku":"T0201",
            "desc":"Test Item #01",
            "qty":1
         },
         {
            "sku":"T0202",
            "desc":"Test Item #02",
            "qty":5
         },
         {
            "sku":"T0203",
            "desc":"Test Item #03",
            "qty":10
         }
      ]
   },
   {
      "date":"2014-02-11",
      "do":"DO140211002",
      "address":"59 Ubi Avenue 1 Singapore 408938",
      "delivery_time":"02:00 PM - 05:30 PM",
      "deliver_to":"Jane Lim",
      "phone":"+6581234567",
      "notify_email":"jane.lim@example.com",
      "notify_url":"http://www.example.com/notify.php",
      "assign_to":"GT1234H",
      "instructions":"Change pass at security counter before proceeding to level 3.",
      "zone":"East",
      "items":[
         {
            "sku":"T0211",
            "desc":"Test Item #11",
            "qty":1
         },
         {
            "sku":"T0212",
            "desc":"Test Item #12",
            "qty":5
         },
         {
            "sku":"T0213",
            "desc":"Test Item #13",
            "qty":10
         }
      ]
   }
]

This is the JSON on the API website but im not sure how to send this from the WooCommerce WC_Class website I have in the function.

Bit new to this so help is appreciated!