There are currently 6.1m children with a CTF in the UK, 78 per cent of which are stakeholder accounts and 17 per cent in cash accounts. Eligible children are those born between 1 September 2002 and 2 January 2011.
Junior Isas were introduced in November 2011 for children born before 1 September 2002 or after 2 January 2011 and allow investment of up to £3,600 per year.
Since then, CTF holders have been "trapped" in accounts offering poor returns in comparison to the new Junior Isa rates.
Danny Cox, head of Financial Planning at Hargreaves Lansdown, said: "Although we don't expect to see any change before April 2014, this is still excellent news – if transfers are allowed it will give the parents of some 6.1 million children greater freedom to choose the best option when saving and investing for their child.
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"CTFs have been in terminal decline since 2011, seeing millions trapped in expensive products or suffering a more restricted investment choice than their Junior ISA counterparts. We expect the consultation should ultimately lead to a full merger of the two products, in the same way that PEPs and ISAs merged."
Tony Vine-Lott, director-general of the Tax Incentivised Savings Association, said: "Allowing the voluntary transfer from a CTF to a JISA for those who choose to do so is a pragmatic and practical solution. The consultation will address concerns about stakeholder protection and allow all the issues surrounding the administration of parallel schemes and the remaining CTF accounts to be explored by Government, industry and consumer groups."
Ian Sayers, director-general of the Association of Investment Companies, said: "Today's announcement is a victory for common sense and consumer choice and will end a two-tier system. Many CTF investors have found themselves "locked" into a product because there is little choice elsewhere. The AIC has long argued that CTFs should be aligned with Junior Isas and we very much welcome today's announcement."

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