The city's ruling Labour group and council social work chiefs have faced strong opposition to the proposals, which will leave just four day-care facilities remaining.
They have now agreed to put forward new plans, which stop short of a U-turn but include significant concessions to work with the people affected to develop alternative ways of offering them support.
The day-care centres will be gradually phased out over a 12-month period, but a new partnership between the council, service providers and users is proposed to give those affected a say in how services are developed.
The council says giving people their own budgets will allow hundreds of people with learning disabilities to participate in a range of activities that interest them.
The proposal, which will be presented to the council's Health and Social Care Policy Committee on March 6, includes a promise that the total amount spent on care budgets for those who currently use day centres will remain the same.
The council also says £3 million currently spent on transport arrangements will also be retained within the social work budget.
Councillor Matt Kerr, executive member for social care, said: "We have looked at the consultation responses very carefully and I am convinced that what we are proposing is the right way ahead.
"Service users who have already moved on from day centres make it clear they do not want to go back."
Councillor Susan Aitken, SNP social care spokeswoman, said the plans were close to what opponents had asked for from the start. She said: "They've obviously taken a lot of the criticism on board."