"We are extremely proud to have been the catalyst for welcomed changes," Elliott added.
The move effectively ends the latest episode of corporate activism that forces strategy changes at big corporate mainstays. Similar battles have seen billionaire Carl Icahn launch a bid for embattled computer manufacturer Dell, while David Einhorn has recently taken on technology giant Apple in an effort to get the company to deploy more of its cash hoard.
For months, Elliott and Hess have been locked in a bruising public battle that initially showed little hope of resolution.
Hess' CEO John Hess said in a statement that the settlement would "provide effective oversight, to ensure that we continue to create meaningful long-term value for all Hess shareholders."
Recently, Hess has moved to reshape a moribund operation that has fallen behind its competition. In addition to stripping John Hess of the company's chairmanship, Hess recently announced a plan to jettison its retail business in part to redouble its oil exploration efforts at a time when U.S. domestic production is surging.
Still, those moves had not done much to satisfy Elliott, which went public with a campaign to install new directors and break up the company in order to force changes at Hess' helm.
"As we have always stated, we believe Hess has terrific assets that should generate outstanding returns for shareholders," Elliott said in a statement. "We are encouraged that there is now a Board and a governance structure in place to ensure delivery of those returns."
Overall, Hess' board will be comprised of 14 new directors.The vote could mean that Hess' board will seat as many as nine new directors once the meeting's results are certified.
—Reuters contributed to this article