The 2 million Scottish Government scheme will cut 190 off a typical home's annual energy bill.
Ministers hope it will also provide a boost to the plumbing industry and help the environment by reducing the amount of carbon dioxide burned in Scotland by 5,600 tonnes, the equivalent of taking 1,700 cars off the roads, heating the water for seven million baths, or heating 1,300 homes for a year.
The initiative is only open to those with the least efficient G-rated boilers, which convert less than 70 per cent of fuel into heat, and which are often owned by people who can least afford to replace them.
In total, 5,000 homes will benefit from the scheme, which will run on a first come, first served basis from 24 May.
Housing and communities minister Alex Neil said: "Through the boiler scrappage scheme, we will help people replace rickety old boilers for new energy-saving models and, importantly, put money back into the pockets of householders. At the same time, we are providing an economic stimulus for the heating industry, supporting jobs and helping it get through this financially difficult time."
Robert Burgon, director of the Scottish and Northern Ireland Plumbing Employers Federation, said: "Installing a new system will not only help the environment, it will also help save money on heating bills. Like many other industries, the plumbing and heating sector has been badly hit by the recession and the scheme will prove a boost to many businesses."
A similar scrappage scheme was introduced in England and Wales in January, and the Scottish Government has been criticised for not introducing it sooner north of the Border. Shadow environment secretary Sarah Boyack said: "I am glad that the SNP are finally doing the right thing by adopting Labour's plans for a boiler scrappage scheme, but they are three months late.
"The first wave of grants was issued to householders in England in January.
"The money was there from the Chancellor to fund the scheme, so there is no excuse for the SNP dragging their feet and leaving so many Scots out in the cold during one of the coldest winters in decades."
Elizabeth Leighton, senior policy officer at WWF Scotland, added: "Home energy use accounts for nearly one-third of Scotland's carbon emissions.
"So it is essential that homeowners are given every opportunity to make their homes more energy efficient if Scotland is to play its part in tackling the climate change."
All the major energy companies which sell and install boilers, including Scottish Gas, E.On, Npower and Scottish & Southern, have matched the Scottish Government's offer, which means householders can potentially receive 800 towards the cost of a new efficient boiler.
The Scottish Government also spent 60m on an energy-assistance package for 33,700 households living in fuel poverty in 2009-10.
HOW TO CLAIM
ANYONE who thinks they qualify for the boiler scrappage scheme should call Energy Saving Scotland.
In most cases, advisers will be able to say over the phone whether the boiler has a G rating and is eligible for replacement, by asking a few questions about its age, make and model.
The Scottish Government does not know how many boilers will qualify for the grant, but anecdotally believe it to be a "significant" number. Vouchers will be awarded after the new boiler has been installed.
The Energy Saving Trust is available on 0800 512 012.