Parkmead has agreed to acquire a further 20% stake in the Athena field in the Moray Firth from Germany's EWE in what Mr Cross said was a landmark deal for the Aberdeen-based company.
"This is Parkmead's most important deal to date," said the oil and gas entrepreneur.
Mr Cross has led Parkmead on an ambitious expansion drive since taking charge of the Aim-listed firm late in 2010. He made around £57m when the Dana Petroleum business he developed was acquired by the Korea National Oil Corporation for £1.9bn in that year.
Under the deal with EWE, Parkmead will triple the size of the holding in the producing Athena field it acquired through the £15m acquisition of Lochard Energy in July.
Mr Cross said the acquisition of the additional interest in the field fits perfectly into Parkmead's strategy to become a key exploration and production player in the North Sea.
"Increasing our oil production three-fold from the Athena field will deliver major growth in the company's revenue and cash flow," he said.
Parkmead could use the cash generated from increased production to fund acquisitions and investment in its existing assets.
The Athena field, which is operated by Ithaca Energy, lies around 100 miles north-east of Aberdeen.
Parkmead said Athena is producing at a reduced rate of around 7500 barrels of oil per day, compared with an average of 9000 bopd in the second quarter of 2012, following some issues with pump operations.
The company said there is a work programme planned for 2014 to increase production and bring it back up to normal levels.
EWE will reduce its direct investment in the North Sea as a result of the transaction.
As the German utility is taking $3.2m of the purchase price in Parkmead shares, it will retain an exposure to Athena. The remaining $8m will be paid in cash.
Separately, Aberdeen-based Faroe Petroleum said drilling has started on the Butch East well in the Norwegian North Sea, in which it has a 15% interest.