"He has agreed to allow all aid workers regardless of nationalities," Ban said in Naypyidaw, Myanmar's capital.
Asked if this was a breakthrough, Ban said: "Yes, I think so."
But the specifics of the new agreement remained unclear and it was not immediately known if Myanmar's rulers would allow in aid from US naval ships nearby - which it said before would be rejected.
UN agencies said they are ready to step up relief to cyclone victims but needed to know practical details of the country's new commitment to admit all aid workers to the devastated coastal area.
Elisabeth Byrs, the UN relief spokeswoman, said UN agencies had been building up food and other supplies for those people affected by the storm but was unable to say immediately how many aid workers would be going into Myanmar.
International aid groups reacted cautiously to the breakthrough, stressing that they would need full access to the devastated Irrawaddy Delta.
"We're not clear on the details - it is welcome news, but we still don't know if this will give us access to the worst hit areas," Chris Webster, from the emergency response team at World Vision, told Al Jazeera.
Lionel Rosenblatt, a former president of refugees international, told Al Jazeera, said he was "sceptical" of the agreement.
"I think if its a precursor to wider agreements then it's something very significant, but we're still not sure what it means in terms of speed - it may take days for these people to get to duty stations," he said.
"I think we have to remember we're now three weeks plus one day into the time elapsed since the cyclone hit - people are in very bad shape."
International relief organisations have repeatedly insisted that more people will die unless they get immediate food, water, shelter and medical care.
The UN Food and Agriculture Organisation warned that hundreds of thousands of people in remote areas of the delta have insufficient food, and said prices for rice, cooking oil and other basics had doubled throughout the country.
Only a "very narrow window of opportunity" remains to provide seeds and other material to farmers before the rice planting season upon which millions depend begins in a few weeks, the agency said.
While accepting thousands of tonnes of donated supplies, Myanmar's rulers have been blocking visas for most foreign disaster management experts and insisted reports of survivors not getting enough aid were the work of "traitors".
A senior UN official present at the meeting between the UN secretary-general and Than Shwe said Myanamar also agreed to allow foreigners to work in the hardest-hit region, the Irrawaddy Delta, which has been virtually off-limits to them.
"The general said he saw no reason why that should not happen as long as they were genuine humanitarian workers and it was clear what they were going to do," the Associated Press quoted the official as saying.
The announcement that Myanmar would halt its restrictions came on day two of Ban's visit, the first by a UN secretary-general in more than four decades.
Despite the continuing misery caused by Cyclone Nargis, the country's military rulers pressed ahead with plans to hold a second round of a referendum on Saturday in areas hit hard by the storm.