About 120,000 two and three-year-olds and about 100,000 primary school pupils will be offered the vaccination - which is given to children using a nasal spray rather than injection - over the 2013-14 flu season.
By towards the end of 2015, about one million children aged between two and 17 will have had the chance to be immunised.
A fifth of the population will be offered a free flu vaccination, with those aged over 65 and those with conditions that put them at greater risk from the disease getting the jab, as well as carers and health and social care workers.
First Minister Alex Salmond launched the programme by receiving the injection himself at a community surgery in Maud, Aberdeenshire.
Mr Salmond said: “Flu is a serious illness and a vaccine is the only way to protect you and those around you. The vaccine is safe, quick, and for those considered at risk, free from the GP. The vaccine is an excellent way to protect you and help stop flu spread over winter.”
He added: “We are committed to help and protect the most vulnerable and at risk groups in society likely to suffer serious consequences of flu. As a result, for the first time this winter we are taking extra precautions to protect families by making sure children are also offered this vital vaccine.
Dr Nicola Steedman, the Scottish Government’s senior medical officer, also stressed the importance of getting immunised against flu.
“Every year we see examples of how devastating flu can be,” she said.
“For those with existing health conditions such as asthma, diabetes, heart or liver problems, flu can result in serious complications. Furthermore, those who are pregnant or over 65 are also at increased risk of flu and its complications and should be vaccinated to help protect against flu, even if they currently feel healthy and fit.
“Flu can also be very serious for children, particularly the youngest ones who have little or no immunity to the infection, which is why we are rolling out the new childhood flu immunisation programme.
“Getting immunised against flu is easy and safe, and it avoids unnecessary worry for you and those close to you.”