Councillors confirmed the investment on Wednesday as part of the authority's budget agreement for the year.
Of this £1.6m is to be spent on improving the choice of placements for looked-after children and £500,000 is to be allocated for strengthening child protection processes and investing in the development of the workforce.
The council has also promised a further £1m to expand the number, quality and choice of short-breaks available for children with disabilities.
Parenting and family support services will receive an additional £500,000 and £100,000 will be put towards improving reviews of care plans.
Stewart Golton, executive member for children's services said: "We have high expectations for the standards of service we provide to children and young people who are in the council's care and to others across the city who are also vulnerable. This investment will enable us to give them, their carers and their families the quality of support they deserve."
The announcement comes just weeks after the council confirmed it would be cutting 650 jobs, sparking concerns about the impact on children and young people's services.
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