It has previously been illegal in the UK to rip songs from a CD to a digital player or transfer eBooks, music, films and games from one device to another.
Business Secretary Vince Cable said the move was "not only common sense but good business sense".
"Bringing the law into line with ordinary people's reasonable expectations will boost respect for copyright, on which our creative industries rely," he said.
"We feel we have struck the right balance between improving the way consumers benefit from copyright works they have legitimately paid for, boosting business opportunities and protecting the rights of creators.""
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