The operation began on Sunday afternoon, nearly a month after the ship hit a reef and capsized off the island of Giglio.
The process had been delayed by both the search and rescue operation and bad weather, prompting fears of a leak into the protected waters off the island.
Seventeen people died when the ship capsized and 15 more are presumed dead.
Captain Francesco Schettino has been accused in Italy of manslaughter, causing a shipwreck and abandoning ship before all those aboard were evacuated.
Prosecutors in France have also launched an investigation, given that four French nationals died and two others are among the missing.
Francesco Schettino, denies wrongdoing.
Dutch salvage company Smit is conducting the operation to pump out the fuel, which is expected to take about four weeks to complete.
It will concentrate on the first of 15 tanks that are believed to hold around 84% of the fuel on board, the AP news agency quoted Italy’s civil protection department as saying.
Valves will be fixed to the tanks, allowing oil to be pumped through a hose on to a crane barge alongside the vessel. From there the oil will be transferred to a waiting oil tanker.
As oil is removed, water will be forced in via a second hose to fill the vacuum.
Image source: Wikimedia Commons President-elect Donald Trump celebrated his election victory at the Ultimate Fighting…
Millions of voters across the US chose to return Donald Trump to the White House…
Donald Trump declares victory in the US election as he addresses jubilant supporters in Florida.…
Stocks around the world are rising as Donald Trump appears to be on the cusp…
Donald Trump has won Pennsylvania, North Carolina and Georgia and taken a lead over Kamala…
Quincy Jones, the celebrated musician and producer who worked with Michael Jackson, Frank Sinatra, Ray…