The UK's largest current account provider, with over 20 million personal current account customers, said more than nine in 10 of those with its brands Lloyds Bank, Bank of Scotland and Halifax will be left either better off or in the same position financially.
Starting in November, customers will be charged a single rate of 1p per day for every £7 of planned overdraft usage.
A fee will be charged at the end of each day of planned overdraft usage, which Lloyds said would help customers to budget, rather than being hit with a bigger bill weeks later.
All fees and charges associated with unplanned overdrafts will be removed.
Lloyds is writing to customers to tell them how they will be affected. The less than one in 10 who will be worse off will receive extra support, which could prompt them to consider a more cost-effective way of borrowing. This may include reviewing alternative options, such as a personal loan.
Those who may be worse off are particularly likely to have large overdrafts which they consistently max out for long periods.
Lloyds said the average debit balance for a customer using their overdraft is £450 in a month.
A Lloyds Bank Classic current account customer using £450 of a planned £1,000 overdraft limit for seven days would currently pay £7.49. But under the new system they would pay £4.48.
A Halifax Reward customer who goes overdrawn by up to their planned £100 limit for 10 days and also goes into an unplanned overdraft by £50 for two of those days will be charged £1.40 under the new system. Previously they would have been charged £18.
The bank expects to make less money overall from overdrafts as a result of the moves, but declined to specify amounts.
It is also automatically opting customers into receiving free text alerts, to help them stay on top of their accounts. People who do not want texts can opt out.
Lloyds Banking Group's changes will also mean that, from November, customers will no longer be charged a "returned item fee" for having payments stopped due to a lack of funds.
Greg Coughlan, the bank's director of personal current accounts and payments, told the Press Association: "We want to put customers in control so that they can better manage their day-to-day finances" with "pay-as-you-go" daily charging.
He continued: "We think more customers will be able to use their overdraft in a smarter way."
Mr Coughlan said that while the banking group expects to see its overall income from overdrafts reduced: "We're convinced we will have better relationships with our customers as a result of the change."
He said that for the vast majority of customers, the charges under the new system would only be "pennies a day".
Vim Maru, group director, customer products and marketing, Lloyds Banking Group, said: "When asked about our new approach, over 80% of customers said that they preferred it compared to the current charging format."
An investigation by Which? into unarranged overdraft fees found some can potentially cost more than a payday loan.
The Competition and Markets Authority (CMA) previously said that in 2014, £1.2 billion of banks' revenues came from unarranged overdrafts.
The Financial Conduct Authority (FCA) is currently putting the high-cost credit sector under the spotlight, including overdrafts.
Peter Vicary-Smith, Which? chief executive, said Lloyds' decision is a "positive step".
He said: "The Financial Conduct Authority must now use its review of high-cost, short-term credit to ensure other banks follow suit, restricting unarranged overdraft charges to the same level as for arranged overdrafts."
Andrew Hagger, founder of Moneycomms.co.uk, said Lloyds had taken a "fairly radical move" and predicted more banks would be reviewing their overdraft charges.
Mr Hagger said Lloyds' new tariff works out cheaper for customers with smaller borrowing requirements.
But for those borrowing sums in four figures it starts to get more expensive, he said - for example a £2,000 overdraft for 12 days currently costs a Club Lloyds customer £17.47 but under the new tariff it is £34.29.
Mike O'Connor, chief executive of StepChange Debt Charity, said around half of its clients have struggled with overdraft debt.
He said: "This looks a positive step forward, but there is a need to monitor what happens next, not least for the questions this announcement poses for the overdraft market as a whole."