The Scottish Government has promised councils £7 million funding this year and has promised to look at future years.
Falkirk Council will also receive its share of £6 million that will allow schools to waive some other charges, such as materials for home economics materials or theatre trips for pupils studying drama.
Councillor Adanna McCue, the portfolio holder for education at Falkirk Council, said it was “fantastic news”.
She said: “I welcome any additional funding that helps children and young people achieve their full potential.
“No matter what their circumstances, they will be given a chance to potentially experience something new and exciting and it will bring so many other benefits to their education.”
At the moment, Falkirk district pupils from P4-S6 pay £160 every year for lessons, although those who are learning an instrument for an SQA qualification do not have to pay.
Falkirk pupils who are entitled to free school meals or a school clothing grant also get lessons free of charge.
A spokesperson for Falkirk Council said that it was too early to say what its share of the funding would be.
They added: “The additional funding is welcome to support more inclusive access to the curriculum for all of our young people.”
Making the announcement, Education Secretary Shirley-Anne Somerville said: “All children should have the best start in life and the ability to take part in core elements of education should never be limited by a child’s ability to pay.
“Today’s announcement means families will not see bills for musical tuition or core curriculum activities in the new school year.”
COSLA Children and Young People spokesperson Councillor Stephen McCabe, said: “Councils recognise the importance of instrumental music tuition for the learning and development of our children and young people.
“Where fees were in place for tuition this is due to a range of local pressures on core council budgets.”
The Scottish Government has now pledged to work with COSLA and local authorities to make sure funding can continue in future years.