Savers will be able to earn up to £1,000 in interest tax-free when a new allowance comes into force on Wednesday.
Coinciding with the new tax year, the new personal savings allowance means that banks and building societies will stop deducting tax from account interest.
Basic rate taxpayers will be able to earn up to £1,000 in savings interest tax-free, while higher rate taxpayers will be able to earn up to £500.
Savings income includes interest from bank and building society accounts, as well as accounts with some other providers, such as credit unions and Treasury-backed National Savings and Investments (NS&I).
It also includes some other types of income, such as that from government or company bonds.
Money held in tax-free Isas will not count towards the allowance as this cash is already ring-fenced from the taxman.
The move should bring some welcome relief to savers, who have suffered the effects of more than seven years of the Bank of England base rate being held at its record low of 0.5%.
According to financial website Moneyfacts.co.uk, savers are facing the worst Isa season on record. The average Isa now pays just 1.29% in interest, a fall from 1.45% a year ago and 2.39% five years ago.
Many current accounts pay attractive rates by comparison, with deals offering interest of 3%, 4% and 5% as well as potential perks such as cashback and cash to join up.
One in 14 (7%) people plan to move money out of their Isa and into another savings account, according to research from AA Financial Services among more than 2,000 people.
But Michael Johnson, director of AA Financial Services, warned savers: "The decision on what to do with your money isn't as simple as comparing rates between saving accounts and Isas."
Mr Johnson said savers should consider how any future increase in interest rates will affect them.
For example, a basic rate taxpayer with £50,000 in a savings account earning 2% will generate £1,000 interest - meaning all interest is protected by their personal savings allowance. But if their rate increased to 3% they would generate £1,500 - meaning £500-worth of interest will become liable to tax.
Any future pay rises could also affect how much of a saver's interest is tax-free. A pay rise taking a saver from a basic rate tax bracket to a higher rate tax bracket would halve their allowance from £1,000 to £500.
An advantage of Isas is that once the cash is put into one, it remains ring-fenced from the taxman until the saver decides to withdraw it. And the annual Isa allowance will increase from its current level of £15,240 to £20,000 from April 2017.
Tom Riley, head of savings at Nationwide Building Society, said it would be "perhaps short-sighted" for people to think Isas are no longer relevant.
He said: "It's not just the here and now where I think Isas are an option because spouses can inherit their partner's Isa allowance upon death, whereas the new personal savings allowance can't be inherited.
"Also, from April 6, the Government is allowing providers to offer flexibility on Isas.
"So, with some providers, you'll be able to replace money withdrawn from some Isa products during the same tax year, without impacting your annual Isa allowance.
"Any withdrawals need to be replaced before the end of the tax year though and you can't carry forward any unused Isa allowance from previous years - so it's a case of use it or lose it."
April's savings shake-up also sees the launch of new Innovative Finance Isas, which will allow savers to potentially boost their returns further. Innovative Finance Isas will be able to hold peer-to-peer loans, which often pay significantly higher returns than cash accounts.
Peer-to-peer lenders act as middlemen, matching people who have some cash to invest with those who want to borrow money.
However, money held with peer-to-peer lenders does not fall under the Financial Services Compensation Scheme (FSCS), which protects savers if their bank or building society goes bust, so investors need to bear in mind the risks.