Mr Pompeo, who met North Korean leader Kim Jong-un during a short trip to Pyongyang on Sunday, said inspectors will be permitted to visit a single missile engine test facility.
The inspectors will also go to the Punggye-ri nuclear testing site “as soon as” the two sides agree on logistics.
Mr Pompeo revealed both sides were “pretty close” to agreeing to details on a second summit.
The news follows the historic summit between US President Donald Trump and Kim Jong-un in June this year.
Trump and Kim Jong-un met in Singapore in what was the first-ever meeting between the leaders of the US and the Democratic People’s Republic of Korea.
State-run media in North Korea said talks with Mr Pompeo had been “productive and wonderful” as they discussed possible steps toward denuclearisation.
A statement from North Korean media outlet KCNA said: “Together with Mike Pompeo, Kim Jong-un appreciated the positively developing situation on the Korean peninsula, explained in detail the proposals for solving the denuclearisation issue and matter of concern of both sides and exchanged constructive opinions.”
The news of the move towards denuclearisation comes after an impasse developed between Pyongyang and the White House as Kim Jong-un refused to give up his nation’s nuclear arsenal.
Now, the North Koreans are appearing to indicate they are happy for international weapons inspectors to visit the Punggye-ri test site to give assurances the weapons have been dismantled.
Mr Pompeo has described his fourth visit to the North Korean capital as “another step towards denuclearisation”.
He also revealed he had a “good, productive conversation” with Kim Jong-un – although he conceded more work needed to be done.
The North Korean leader is also expected to visit Russia soon, South Korean President Moon Jae-in said on Monday.
Meanwhile, Chinese leader Xi Jinping is also predicted to travel to North Korea in a sign of thawing relations.
Moon Jae-in spoke of the imminent travel plans of the North Korean and Chinese leaders during a Cabinet meeting a day after Mr Pompeo travelled to North Korea, but did not elaborate further.
The South Korean leader spoke positively about Mr Pompeo and Kim Jong-un’s meeting, saying it set up conditions that could make another summit between Washington and Pyongyang possible.