Instead of a total annual Isa allowance of £11,520, only half of which can be held in a cash account, the annual limit will be raised to £15,000, without restrictions.
George Osborne said: "We will make Isas simpler by merging the cash and stocks Isas to create a single new Isa. We will [also] make them more flexible by allowing savers to transfer all of the Isas they already have from stocks and shares Isas into cash or the other way around."
The Chancellor announced a new Pensioner Bond would be available from National Savings and Investments in January 2015, four months before the General Election.
The bond's rates will not be set until the autumn, but are likely to be 2.8% for a one-year term and 4% for three years, giving over-65s the best rates in the market.
The annual £30,000 allowance for saving into Premium Bonds will rise to £50,000 next year.
Mr Osborne confirmed that from April 2015 the starting rate of tax for savings income, such as bank or building society interest, will be cut from 10% to zero.The maximum amount of taxable savings income eligible for this starting rate will be increased from £2880 to £5000.
The Low Incomes Tax Reform Group said it was "great news for prudent savers on modest incomes".
The increased Isa limit will come into force on 1 July. The limit on Junior Isas will also be lifted from £3720 to £4000, and switching restrictions are scrapped, although transfers from Child Trust Funds into Junior Isas will still not be allowed until April 2015.
Paul Johnson, director of the Institute for Fiscal Studies, commented: "The big gainers will be those who have a fair amount to start with. But people with the lowest level of savings tend to have the most in cash, which has up until now been the most heavily taxed."
Over half of savers utilising the maximum cash allowance in 2013 had incomes of less than £20,000, and this group holds an average £15,000 in their cash Isa, according to the Halifax.
Graham Beale, chief executive of Nationwide Building Society, was delighted at "much-needed support for ordinary savers" after years of campaigning.
He said: "It will reduce confusion on the differing amounts which could be saved in cash and stocks and shares and more importantly give people more flexibility to earn tax-free interest.
"It is particularly good for first-time home-buyers who can now save even more towards their deposit in a tax-efficient ISA."
Mr Beale called allowing the transfer from stocks and shares Isas into cash Isas "great news", helping those nearing retirement and pensioners who prefer to have their savings in cash.
Neil Lovatt, product director at Scottish Friendly, said: "Today's announcement could help facilitate a much-needed shift from borrowing and into saving."
Danny Cox, head of financial planning at Hargeaves Lansdown, said a single allowance would mean anyone holding cash in a stocks and shares Isa would now escape 20% tax. He noted corporate bonds and gilts would no longer be restricted to five-year maturities.
However Martin Lewis at Moneysaving expert.com claimed even at the best of today's cash Isa rates, the extra headroom for cash savings would only give an £19.
Anna Bowes of website Savers Champion welcomed the reforms but said: "A £15,000 Isa is of little benefit if the interest rates being paid are still derisory - we desperately need competition to return for rates to improve."
Saving with social or peer-to peer-lenders such as Zopa and business lender Funding Circle will also become eligible within an Isa, though not immediately.
James Meekings, co-founder of Funding Circle, said: "The inclusion of peer-to-peer lending in Isas ensures British people earn inflation-beating, tax-free returns whilst helping support the country's economic recovery."