Ian Hannam, a former JPMorgan Chase & Co. banker who served for decades in an elite unit of the British Army Reserve, signed contracts in Washington on Friday to start exploration of gold and copper deposits in northern Afghanistan.

Mr. Hannam, once known as the “King of Mining” in the British press for his role in deals involving mining giants such as BHP Billiton Ltd. and Xstrata PLC, is among the first to secure such contracts under the Trump administration.

Mr. Hannam told the Wall Street Journal that the Trump administration’s renewed focus on Afghanistan’s mineral wealth helped push the government to finalize the deals.

President Donald Trump spoke to the Afghan President Ashraf Ghani last September to send a message that Afghanistan’s natural resources, including large deposits of copper, iron ore and gold, should help pay for the war.

The two leaders agreed that U.S. companies should be brought in despite a formidable list of challenges, including rampant corruption, insecurity and poor infrastructure.

U.S. officials have long hoped that the country’s natural resources could eventually become a source of revenue that would close the government’s budget deficit. The U.S. government has estimated Afghanistan’s mineral wealth may be close to $1 trillion. A briefing paper released by the Pentagon in 2010 listed minerals including copper, gold and lithium, among others.

“There’s a realization that… [mining] is one of the only ways to close that revenue gap,” Mr. Hannam said, adding that he was eager to invest in the mineral deposits back in 2010. “We’re just happy to have got there.”

The deals, signed with Afghanistan’s acting minister of mines, Nargis Nehan, will grant Centar Ltd., Mr. Hannam’s U.S.-based mining investment company, rights to develop the projects that have been stalled since 2012 because of disagreements with the government.

Mrs. Nehan didn’t respond to a request for comment. The White House National Security Council deferred comment to the State Department. A State Department official said the deal was an encouraging development for Afghanistan’s economy.

The Badakhshan Gold Project is located in the northeastern Afghanistan. The Balkhab Copper Project lies in the north, near the country’s only railway on the border with Uzbekistan.

Centar plans to start work on the site in early 2019, Mr. Hannam said. If the deposit is found to contain significant deposits of gold, it could start production within a 18 months and become fully operation within three years.

Mr. Trump made mining a priority after inheriting the 17-year war in Afghanistan, which has cost some $126 billion in reconstruction funds as well as more than $1 trillion in military expenses since the start of the war, according to estimates from various think tanks.

However, Afghanistan, long known as the “graveyard of empires,” also could prove to be a graveyard for mining deals. Security lapses, threats by insurgents, geographic isolation and government corruption are among the problems that have scuttled previous attempts to develop the mineral resources in the country.

A Chinese deal to develop a $3 billion copper mine at Mes Aynak, southeast of Kabul, in 2010 stalled in the earliest stages of work at the site. An Afghan government deal with an Indian consortium to develop a $11 billion iron ore mine in 2011 fell apart before it even started.

In the north, an oil joint venture between an Afghan company and state-owned China National Petroleum Corp. has been stopping and starting for years, and has yet to start serious exploration.

Mr. Hannam worked as an adviser to the Department of Defense and said he was unable to persuade any major Western company to bid for the asset in Mes Aynak, which geologists say could be one of the world’s major deposits of copper.

“If that asset was anywhere other than Afghanistan, it would have been built by now,” Mr. Hannam said. “The two things that mining companies care about is the stuff in the ground, potential, and the above ground risk.”

Mr. Hannam said the experience led him to create Centar, to prove to Western companies that Afghanistan can be worth the risk. Centar won a deal to explore for gold in Baghlan, north of Kabul, in 2008, but didn’t find a significant deposit that was worth producing, he said.

The equipment remains in country and can be used for the new projects.

Mr. Hannam’s theory remains to be tested at a time when Afghanistan’s political future could not be more uncertain.

Despite an increase in U.S. military support for local forces, the war has remained stalemated and the Taliban-led insurgency is returning to power outside major cities. Observers have expressed concern over parliamentary elections scheduled later this month, already three years overdue. In Washington, officials are beginning to scenarios including the possibility of a disputed parliamentary election, forcing the delay or cancellation of the presidential elections next year.

Mr. Hannam said that mining companies often operate in areas with fraught political risks and that the rewards in Afghanistan make the venture worthwhile.