U.S. authorities declared a moratorium on deepwater drilling in the Gulf in May 2010 after the Macondo well, drilled for BP by Transocean's Deepwater Horizon rig, spewed millions of barrels of oil into the sea.
The drilling ban was lifted in October 2010 but U.S. regulators did not issue permits to restart drilling until the end of February this year.
Maersk Drilling, a unit of Danish shipping and oil group A.P. Moller-Maersk , said its Maersk Developer semi-submersible rig picked up anchors on March 21 and began its journey to its new location in the Gulf of Mexico.
"Once there, the rig is planned to drill the first new deepwater exploration well to be drilled since U.S. authorities imposed a moratorium on drilling activities in the wake of the Deepwater Horizon accident," it said in a statement.
The Maersk Developer will bore an exploration well for Exxon Mobil (XOM.N) at its Hadrian prospect, a Maersk Drilling spokesman said.
The rig remains on a four-year contract to Norway's Statoil (STL.OL) which has sublet it to Exxon, which will pay the same rate as Statoil, the company said.
Maersk Drilling Chief Executive Claus Hemmingsen declined to specify what rate Exxon Mobil would pay for the rig, but added: "We are happy about the rate."
"It was fixed at a time when there was good demand for deepwater rigs," Hemmingsen told Reuters.
Hemmingsen said the U.S. ban on deepwater drilling in the Gulf of Mexico had cost Maersk Drilling about $20 million.
Maersk Drilling, with a fleet of 26 rigs serving oil companies around the world, made a net profit of $399 million on revenues of $1.63 billion in 2010.
"We expect to see an increasing demand from oil companies for modern equipment and good safety procedures," Hemmingsen said in the statement.
Shares in A.P. Moller-Maersk traded down 1.9 percent by 1506 GMT, underperforming a flat Copenhagen bourse .OMXC20.