Earlier this week the Government announced the decision following a consultation launched in the 2013 Budget.
It hopes to bring in legislation to make the first transfers possible by April 2015.
Ian Sayers, director general of the Association of Investment Companies, said: "This long-awaited announcement is a boost for consumer choice and ends a two tier system for children's saving.
"Many Child Trust Fund investors have found themselves 'locked' into a product because there are few alternatives but now they will have the freedom to invest in a far wider range of vehicles."
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CTFs were launched by the Labour Government and babies born from September 2002 received an average voucher of £250.
But the funds no longer received Government contributions after 2011 when Junior Isas were introduced.
Moving money from CTFs to Junior Isas has previously not been allowed.
Mr Sayers said: "The creation of a single Junior ISA market is a great opportunity for the investment company industry.
"Investment companies can be an ideal way to save for children and are particularly popular for this purpose."
The Treasury said that while it will allow cash transfers it will not permit mergers of CTFs and Junior Isas.