The new rules, published Monday by the central bank, come months after the government revoked the licences of around 100 bureaus and temporarily shut a newspaper for using unofficial data on exchange rates.
President John Magufuli has said that the central bank had previously licensed too many bureaus and some of them had breached laws.
The Tanzanian shilling has been broadly stable since the beginning of the year and the International Monetary Fund said in an April report that the real value of the currency is "broadly in line with fundamentals".
But the IMF also warned of serious weaknesses in official data and said that some indicators point to slower pace of economic activity than reported by the government.
Since February, when the bureaus were shut, commercial banks have conducted the bulk of foreign currency trading.
The Bank of Tanzania governor said this month that, due to the reduced number of exchange bureaus, around $10 million was traded daily by commercial banks, a change which he said has increased transparency in the market and improved hard currency inflows.