Mr Obama issued the executive order weeks after meeting Myanmar's de facto leader, Aung San Suu Kyi.
Myanmar's access to trade benefits for poorer nations was suspended in 1989 over human rights abuses.
But the White House said substantial advances to promote democracy meant that it was no longer a threat to America's national security.
Correspondents say the move is designed to coax the rapidly transforming South East Asian country from decades of economic isolation as Ms Suu Kyi's government manages the difficult transition to democracy in Myanmar, also known as Burma.
"While Burma faces significant challenges, including the consolidation of its democracy, the United States can, and intends to, use other means to support the government and people of Burma in their efforts to address these challenges," Mr Obama wrote in a letter to the US House and Senate speakers.
However, while many companies will now enjoy lower tariffs, there are some sanctions which remain in place.
A "blacklist" of at least 100 companies and individuals with links to the former military junta has been scrapped, although a few individuals will remain sanctioned.
Myanmar was run by an oppressive military junta from 1962 to 2011.
Ms Suu Kyi, who as opposition leader was kept under house arrest for 15 years, led her National League for Democracy party to victory in Myanmar's first openly contested election for decades in November 2015.

Newspaper L'Equipe reported that the pair, along with winger Juan Imhoff, tested positive for corticosteroids before playing in June's Top 14 final.
Racing say the case relates to "treatment by an authorised channel".
They added: "We're on the side of law, ethics and love of a clean sport."
The statement came after Carter and Rokocoko's agent told the New Zealand Herald he had assurances "all the documents around TUEs were in place".
TUEs allow sportspeople to take prescribed medicines - which are otherwise be banned for their performance-enhancing properties - if there is a medical need.
"As far as I know today, there was no request [for TUEs] made ahead of time, but people are allowed to regularise these things after the event," French Sports Minister Patrick Kanner said on France Info radio.
Fly-half Carter, 34, and winger Rokocoko, 33, scored 20 points between them as Racing Metro beat Toulon 29-21 in Barcelona.
Argentine wing Imhoff, who has scored 21 tries in 35 Tests, was also part of the starting line-up at the Nou Camp.
Carter, man of the match in the Top 14 final, played 112 Tests for New Zealand and was part of the All Blacks side which won the 2015 Rugby World Cup.
He is widely regarded as one of the greatest players in the history of the game.
Rokocoko scored 46 tries in 68 Tests between 2003 and 2010.

Tata Steel closed its Dalzell mill in Motherwell and the Clydebridge plant in Cambuslang with the loss of 270 jobs.
Both were later bought by international metals firm Liberty House which intends to restart production at the Motherwell site in September.
About 60 staff are currently working there, with 40 more recruits expected - many of them former Tata Steel staff.
Liberty Steel said that the Dalzell plate-rolling mill had taken delivery of about 1,500 tonnes of slab steel rom the British Steel plant at Scunthorpe.
This is in preparation for the restart of steel plate production next month.
Jon Bolton, chief executive of Liberty Steel UK plate division, said: "This is a significant milestone for the plates business in Scotland, but also positive news for the UK steel sector as steel once again is manufactured in British Steel's Scunthorpe site to be rolled in Scotland.
"It is pleasing to watch the plant gradually coming back to life as more people arrive on site and particularly pleasing to welcome young apprentices to the team."
Liberty said that about 60 staff were involved in the preparations to reopen Dalzell, with a further 40 expected to join the workforce before production starts.
The firm said that about 70% of the initial wave of recruits were former employees returning to their old jobs.
It has also awarded about 20 new supply contracts, for business and engineering services, to firms in the Motherwell area.
Liberty House Group executive chairman, Sanjeev Gupta, said this was the beginning of the fulfilment of a promise to the local community.
"We said we would revive this historic steelworks and that is exactly what we are doing," he said.
President Barack Obama has formally eased long-standing sanctions on Myanmar.
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French side Racing 92 say former All Blacks Dan Carter and Joe Rokocoko did not have therapeutic use exemptions (TUEs) for "anomalous" drugs tests but insist the players have not done wrong.
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Steel production is set to resume next month at one of two Lanarkshire plants that were mothballed last year.