But only four of the 16 newspapers granted licenses by the Ministry of Information have been printed and are on sale, a report by the BBC said.
Even so, it's a major shift toward a more open society by the elected government of former junta leader and now civilian President Thein Sein in early 2011.
The media scene in Burma -- Myanmar's former name -- changed when the military took power in the former British colony in 1964.
Increasing censorship, police harassment and jail sentences for editors, publishers and owners ensued. Some weeklies were allowed, as well as some private sector-government publications and openly junta-linked newspapers.
But the government -- drawn from an elected Parliament -- announced in December that from April private newspapers would be allowed to publish after being granted a license from the Ministry of Information.
Easing of restrictions started in August when the government announced it was halting prepublication censorship, which had been applied to everything from newspapers to song lyrics, fiction, poems and even fairy tales.
Publishers previously had to provide copies of publications to the ministry before publication -- one of the methods of control used by the military junta before it handed over to an elected Parliament.
However, the foreign media in Myanmar remain under tight control about where they may travel, a report by New Delhi news agency Mizzima said.
Many new daily publications will have modest print runs until they are assured of their market as well as how to overcome the lack of distribution to rural areas, the BBC said.
Golden Fresh Land, printed in Yangon, started printing this week and will be looking at better distribution, a report by The Myanmar Times, a weekly newspaper, said.
"There will be some difficulties in distributing papers across the country and not everyone will be able to buy a paper every day," the Times quoted Golden Fresh journalist U Myint Kyaw as saying.
There remain many hurdles before a more recognizably free media by Western standards are in place, including getting rid of the notorious 1962 Printing and Registration Act.
Under the act, failing to register a publication carries a jail sentence up to 7 years and the government can revoke a publishing license at will.
But old censorship habits die hard, a report by the Democratic Voice of Burma, a broadcaster in Norway, said.
In an interview with DVB last month, a government representative said a "supervisory committee" of senior government officials, including military intelligence, was formed to replace Myanmar's censorship board.
The committee carries out many of the same functions include monitoring media output and revoking publication licenses, the spokesman said.
Nonetheless, the government is consulting with the country's increasingly active fourth estate on other issues.
The government is looking at draft legislation prohibiting publishing on numerous topics, including those deemed to "violate" Myanmar's controversial 2008 constitution -- the government's touchstone for creating an open society -- and on issues that "inflict damage" between ethnic groups.
Also, a much-delayed print media law drafted by the Ministry of Information likely won't be submitted to Parliament until July because the Interim Press Council was given permission to write its own version for consideration by the government.
The 20-member IPC, officially called the Myanmar Core Press Council, is chaired by a retired Supreme Court judge and includes academics, lawyers and members of press associations.