Senator Philip Ozouf announced the new legislation at the island's first finance technology conference.
The government has been working on the legislation for about 18 months and focused on protecting against money laundering and financial crime.
Virtual currency companies will face tighter regulation as they grow.
John Harris from the Jersey Financial Services Commission said they would not have to pay a fee or face tougher regulation until they had an annual turnover of Â£150,000.
Robbie Andrews, who founded a group to campaign for Bitcoin regulation, said there were already companies waiting to move to Jersey.
He said: "The fact that the government has taken a light-touch approach where other jurisdictions have gone all-encompassing with regulation will be a benefit to Jersey."
Mr Harris said when looking at the regulation they had to be careful about the risk to the finance industry.
Bitcoin expert Dave Birch said Jersey was right to focus on regulation, as it was the area where it could have a competitive edge.
He said: "The barriers most of the companies we work with come from the regulatory environment.
"Everybody can access Bitcoins and it is hard to see how you can get a competitive advantage when you don't have the same scale as other areas such as Silicon Valley.
"Where Jersey has an advantage is being able to connect the regulatory environment to those new key technologies."
Officials hope the new legislation will be in place by the end of the first quarter of next year.
Jersey's government is to introduce "light touch" regulation for virtual currencies, according to the assistant chief minister.