The former junta-run nation last month awarded telecom licences to Norway's Telenor and Qatari firm Ooredoo as it tries to raise telephone coverage from less than 10% currently to 80% by 2016.
The state-run New Light of Myanmar newspaper said the bill had been approved by parliament.
MP Phone Myint Aung said the move would mean "international operators can launch their operations. They are waiting for this bill."
The bill still requires the signature of President Thein Sein to come into effect.
"We have not yet had an opportunity to review the legislation but look forward to the final approval of the Telecommunications Law and to also reviewing the implementing regulations," Telenor said.
"A clear and stable regulatory and legislative framework that ensures predictability and a level and transparent playing field is important for a long-term investor such as Telenor."
Telenor added that it was still finalising the terms and conditions of the licence.
The bid process has been closely watched as a bellwether of economic reforms aimed at driving rapid foreign investment in the nation, which has seen sweeping changes since a quasi-civilian government replaced the military regime in 2011.
Ooredoo, formerly known as Qatar Telecom, this month pledged to introduce "affordable" phone services to Myanmar next year as it pumps US$15bn into the country as part of its 15-year 3G licence.
Few can currently afford mobile phones and SIM card fees, which in the past cost about US$200, although the government is trying to make prices more affordable.
In April state-owned giant Myanmar Post and Telecommunication announced it would start selling SIM cards for less than US$2, and the authorities have begun selling them on an lottery basis.
Another report in Wednesday's state media said one such lottery in Pyinmana, on the outskirts of the capital Naypyidaw, had selected "slow vehicle drivers" as the recipients of its budget SIM cards.
Naypyidaw's council has sold 95 cheap SIMs to "pony cart and trishaw drivers" in the area, the report said.
Source: AFP, via I-Net Bridge
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