All of Swansea Council's key services, like education and social care, can expect "record investment" in 2022-23, its leader has said.
Cllr Stewart also said a council tax rise below 2% was very likely - less than in recent years.
Budget proposals have been drafted following a generous Welsh Government settlement for Welsh authorities.
The provisional settlement allocates £386.5 million to Swansea in 2022-23 - that's £33.9 million more than the current year and a rise of 9.3%.
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It's still early days in the budget-setting process, but the provisional rise from Cardiff Bay is significant because the settlement dwarfs the revenue local authorities raise through council tax and other means.
A report going before Swansea's cabinet on January 20 said that once the Welsh Government's settlement was confirmed, the budget proposals "will show overall substantial net cash investment into all services".
Cllr Stewart said this level of investment hadn't been experienced since the council came into being in its current form in 1996.
"This is record investment for Swansea Council," he said.
But set against the projected £33.9 million uplift are rising costs and other financial pressures facing the council which come to £40 million in 2022-23. They include a forecast pay rise of 3% for all council staff.
In order to set a balanced budget, finance chiefs have proposed plugging the bulk of the £6.1 million shortfall with savings and income-generating measures. These will be subject of a public consultation.
The measures proposed include school transport savings, higher parking charges linked to city centre regeneration, additional income from commercial lettings, and a reduction in residential placements for vulnerable young people.
The report said five full-time council jobs were at risk.
The financial modelling also assumes an extra £1.3 million being raised through income tax, but the final percentage increase - or otherwise - which councillors will debate when they set the budget is not known yet.
Neath Port Talbot and Bridgend councils have proposed a council tax freeze in what is a local Government election year.
Swansea's Labour administration has prioritised schools and social care despite - until recently - dwindling budgets and rising costs.
At the same time it has borrowed heavily to invest in city centre regeneration projects like the new indoor arena, and is also funding new schools in partnership with the Welsh Government.
The cabinet report said a further £20 million had been added to the sum borrowed by the council to date.
LOCAL ISSUES
It also outlined risks on the horizon, such as how long the Covid pandemic might continue, the economic effect of Brexit on local Government, and the cash uplift from the Welsh Government not being repeated to the same extent in future years.
On the plus side, Cllr Stewart said there was further headroom because the council ended up with millions of pounds to spare at the end of the 2020-21 financial year, part of which is being invested as part of a Covid recovery plan.
A report with updated proposals will be published after the consultation, prior to the budget being set at a meeting of full council on March 3.
Speaking earlier this month when the provisional local Government settlement was announced, Wales's Finance Minister Rebecca Evans said: “This is a good settlement for local Government. It provides local authorities with a stable platform on which to plan their budgets for the coming financial year and beyond."
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