Webb then flew to Yangon to meet Nobel peace laureate Suu Kyi at a government guesthouse near her home -- her first meeting with a foreign official since her house arrest was extended by 18 months earlier this week.
Webb's office later issued a statement in Washington saying he had secured an agreement from the junta to release John Yettaw, who was jailed for seven years this week over an incident in which he swam to Suu Kyi's lakeside home.
"I am grateful to the Myanmar government," Webb was quoted as saying in the 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 said.
The statement said Yettaw would be officially deported Sunday morning, adding that "Senator Webb will bring him out of the country on a military aircraft that is returning to Bangkok on Sunday afternoon."
A Myanmar official confirmed Yettaw's deportation.
"Yettaw will be deported and leave with Webb," the official said, speaking on condition of anonymity.
Webb had also urged Myanmar's military regime to free Suu Kyi, who has spent most of the last two decades under house arrest, the senator's office said.
She was driven to the meeting with Webb from her crumbling mansion in a convoy comprising her car and several police vehicles, witnesses said. She left the guesthouse about 45 minutes later.
The Myanmar regime sparked international outrage when a court in the army-ruled nation convicted Yettaw and Suu Kyi over the May incident in which the American swam uninvited to her home.
According to earlier reports, Webb was not due to meet Yettaw, a diabetic and epileptic former military veteran who is being held at Yangon's notorious Insein Prison. Yettaw was hospitalised earlier this month after suffering a series of fits.
Dissident groups have warned that Webb's visit could be manipulated by the Myanmar government to "endorse" its treatment of Suu Kyi and the more than 2,100 other political prisoners in the country's jails.
The UN Security Council issued a watered-down statement Thursday expressing "serious concern" about her detention, while the European Union the same day extended sanctions against the junta, including the judges in the trial.
Critics have accused the junta of trumping up the charges to keep Suu Kyi locked up during elections next year, and of using the polls themselves to legitimise their grip on power since 1962.
The junta refused to recognise the NLD's victory in elections in 1990
Both the White House and State Department welcomed Webb's trip, even though it was officially being made in a private capacity by the senator, the chairman of the Senate Foreign Relations subcommittee on East Asia and Pacific affairs.
The Obama administration said earlier this year that it was reviewing his predecessor George W. Bush's tough stance on Myanmar, even though Obama recently renewed sanctions against the regime.
Webb, a gruff Vietnam veteran, said in April that Washington should seek "constructive" engagement towards Myanmar with the aim of lifting sanctions, while admitting in July that the Suu Kyi trial made it more difficult.
Webb, 63, has written six novels and served in the late 1980s as secretary of the US Navy under Republican President Ronald Reagan.
Than Shwe has, meanwhile, been a long-term bete noire of the United States. A former postman, he has ruled Myanmar since 1992 with an iron-fist, ruthlessly suppressing his rivals.
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