Mrs Clinton announced the move during talks with Burmese President Thein Sein at the United Nations General Assembly
She said the move - the latest in a series - recognised "continued progress toward reform" in Burma.
Earlier, the speaker of Burma's parliament told the BBC that his country's reforms were "irreversible".
Shwe Mann, a powerful figure who recently had US sanctions
against him lifted, said the government intends to establish a
multi-party democratic system and market economy.
Then Sein - the former top general who now leads a nominally
civilian government following elections in November 2010 - is due to
speak at the UN General Assembly on Thursday.
Under his administration many political prisoners have been
freed and censorship eased. The Aung San Suu Kyi-led opposition is now
part of the political process and holds a small number of seats in
parliament.
"In recognition of the continued
progress toward reform and in response to requests from both the
government and the opposition, the United States is taking the next step
in normalising our commercial relationship," Mrs Clinton told the
Burmese president.
She said she hoped the move would give Burmese people more opportunities to sell to the US market.
Thein Sein said he appreciated the move - which is the latest
in a series of such steps since the process of reform in Burma got
under way. The US lifted a ban on investment in Burma in June.
Both the president and opposition leader Aung San Suu Kyi are currently in the US.
Earlier this month, Ms Suu Kyi - who spent years under house
arrest - received a top honour, the Congressional Gold Medal. She had
also called for the sanctions to be eased.
In Burma's commercial capital Rangoon, a spokesman for her
National League for Democracy party welcomed the move, saying it would
be "good in the long term".
Mrs Clinton said consultation on additional steps would
continue. Thein Sein still faces opposition within Burma's military to
political reform, observers say.
But Shwe Mann, the Burmese speaker, described a good working relationship with Ms Suu Kyi.
Speaking to the BBC in Singapore, he said: "She is not my
enemy, and I am sure I am not hers. She has good qualities and she loves
her country. We share the same ambition - to serve the nation and
people."
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