He is the latest Western official to visit Burma since the country embarked on a reform programme last year.
The EU is competing for trade and investment opportunities in Burma now that most sanctions have been lifted.
Mr Barroso is also likely to raise the plight of the Rohingya minority with both the government and the opposition.
In recent months, violence between the mostly Muslim Rohingyas and Buddhists in Rakhine state has forced 100,000 from their homes.'Peace centre'
Mr Barroso will meet President Thein Sein, who has acknowledged that attitudes towards the Rohingyas must be changed, as well as opposition leader Aung San Suu Kyi, who has so far said little about the unrest.
Over the past decade, trade links and aid between the EU and Burma have been a fraction of those with other Asian countries.
EU member states had imposed tough sanctions on the military because of repressive military rule.
In the wake of the country's reform programme, the EU is now offering around $200m (£125m) in development aid over the next year, almost as much as it has given in the past 15.
The EU is also offering Burma the same trade privileges that other low-income countries get.
It will also fund a new "peace centre" to help Burma resolve the long-running conflicts between central government and ethnic minorities.
Source BBC News:
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