The Wireless Telegraphy Act of 1949 forbids the use of radio equipment without a licence or an exemption.
But the gadgets are now expected to become legal to use - without a license - by 2007.
Liberal Democrat culture, media and sport spokesman Don Foster said: "I am delighted Ofcom have ended this ludicrous ban, based on 1940s legislation... which threatened two years imprisonment to music lovers using iTrips.
"This decision... will not only regulate a booming black market and provide the country with valuable tax revenue, but also enable the iPod generation to enjoy their music using the latest gadgets."
Gadget magazine T3 deputy editor Jason Jenkins also welcomed the proposed legalisation.
"They are nifty little things and an easy way to listen to your iPod tunes in your car," he said.