Officials in Myanmar had previously said that Yettaw would probably be deported soon after Webb's departure.
Yettaw, a diabetic and epileptic former military veteran, is being held at Yangon's Insein prison. He was convicted along with Aung San Suu Kyi, a pro-democracy leader, after swimming uninvited to the Nobel laureate's lakeside home.
"I am grateful to the Myanmar government for honouring these requests," Webb said in a statement.
"It is my hope that we can take advantage of these gestures as a way to begin laying a foundation of goodwill and confidence-building in the future."
Webb was also allowed to hold talks with Aung San Suu Kyi, the first foreign official permitted to see her since she was sentenced to 18 more months of house arrest on Tuesday.
Webb said he urged Myanmar's ruling generals to free Aung San Suu Kyi.
Webb was on the second day of his visit to the Southeast Asian nation and arrived in Naypyidaw on Friday for the second leg of a two-week tour of the region.
Advocate of talks
Webb, a Vietnam veteran and former journalist who has reported from across Asia, is a longtime advocate of taking a new approach to Myanmar.
In March he called for direct talks between the US and Myanmar.
But last month, he said the recent trial of Aung San Suu Kyi made it difficult for Washington to pursue "meaningful relations" with Myanmar.
Yettaw triggered the trial when he swam to her home in Yangon in May.
The convictions have been widely criticised around the world, particularly by the US government.
The White House has said Webb's visit would convey "strong" US views of good governance to Myanmar's leaders.
"We welcome Senator Webb's trip to the region, including the stop in Burma," Mike Hammer, a spokesman for the National Security Council, said, using the country's previous name.
Meanwhile, Larry Jagan, a Southeast Asia analyst, told Al Jazeera that "there is a danger in reading too much into this visit. We can't say there's going be a major shift in policy for the Obama administration and the Myanmar government/
"But this visit is extremely important because not even the UN envoy to Myanmar [Ibrahim Gambari] gets to see Than Shwe," he saod.
"It is important for the Burmese leadership to hear of the strong views of American political leaders about the path it should take toward democracy, good governance, and genuine national reconciliation,
David Streinberg, a professor of Asian studies at Georgetown University in Washington DC, said:"I think Senator Webb has wanted to go to Burma [Myanmar] for quite some time and the release of John Yettaw was an example of an effort by the Burmese government to seek better relations with the US.
"Now, they do this rather ham-handedly, I must admit, but at the same time if you really think about this, Senator Webb has released Yettaw, he has seen General Then Shwe, he has seen Suu Kyi," he told Al Jazeera.
"Ban Ki Moon, the secretary general of the United Nations, couldn't do that.
"What has been happening now in Washington has been very good. It's the first time in 18 years that we've had dialogue on Myanmar before."