In a shake-up in the way that Ofcom handles radio spectrum allocation, the organisation will no longer try and ban devices like the Belkin Tunecast.
Such devices convert media player output into very low power radio broadcasts that can be picked up by headphones and other devices.
"Equipment previously available carries a high risk of interference to other broadcast services," said Ofcom.
"However, in response to consumer demand, Ofcom has led negotiations in Europe to develop a harmonised technical approach designed to limit the potential of interference to other wireless devices."
The permitted devices will have to carry an EU CE mark to show that they are the same, but consumers are free to choose how to listen to their music.
The laws on citizen's band radio are also being changed so that users no longer need a licence to broadcast.
Some 20,000 people currently have CB licences after the equipment was decriminalised in the mid-1980s. Ofcom claimed that the rule change will cut the administrative burden which the system imposes.