Children's services in the city have consistently been rated "inadequate" by Ofsted.
Lord Warner was appointed as an independent commissioner last year to oversee attempted improvements.
On Monday the council's cabinet approved plans that will see an extra Â£94m spent over three years.
It includes Â£27.5m already announced for the 2015-16 financial year.
New IT and upgrades to existing systems are also to be introduced, including mobile devices for all social workers.
Under the plans, the number of front-line social worker posts will increase from 511 to almost 600 by March 2017.
The authority has struggled to recruit enough social workers over recent years, particularly those with substantial experience.
Councillor Brigid Jones, in charge of children's services, said the authority had previously relied on "emergency measures" to tackle staff shortages and the latest plan allowed it to approach the matter more "more strategically".
"The biggest thing we need to get right is the recruitment. It's about getting the right staff here and keeping them," she said.
Lord Warner is expected to publish his own report into the state of children's services in Birmingham next month.

The 66-year-old republican from County Louth denies nine tax evasion charges.
The prosecution's case is that he had significant dealings in relation to cattle and land and received farming grants, but failed to make tax returns.
A court in Dublin heard a third day of closing submissions on Tuesday.
Mr Murphy's defence barrister told the Special Criminal Court that "fair analysis" of the evidence should lead to the conclusion it was the accused's brother, Patrick Murphy, who ran the farming operation and controlled the finances.
"I am suggesting that the person in charge of this farming enterprise was Patrick Murphy; that the profiteer was Patrick Murphy; that the chargeable person was Patrick Murphy," the barrister said.
"I am not suggesting that Thomas Murphy was not about the farm. But there is a big difference between growing up in a farming environment and being about the place doing bits and bobs and being the chargeable person, being the actual farmer in charge."
The three judges in the non-jury trial were told the case has been built on hearsay evidence and that key financial documents found inside Patrick Murphy's house had effectively been "buried" because they "didn't suit".
"When you scratch below the surface the reasonable doubt lurks just below the surface, and so does Patrick Murphy," the defence lawyer  said.
It was also claimed the state was seeking to "galvanise" the suggestion Thomas Murphy received a farming income.
"It simply isn't there," the lawyer said.
The inclusion of "business drawings" for items like food, presents, watch repairs, boots and tickets to Paris should also deposit doubt in the minds of the judges, the barrister said.
"That's the height of the prosecution case. It reached the stage that it was utterly ludicrous," he added.
Allegations that Mr Murphy, of Ballybinaby, Hackballscross, had access to large sources of cash were also rejected.
The trial continues.
Extra social workers and new IT systems are to be introduced in a bid to improve children's social care in Birmingham.
[NEXT_CONCEPT]
The case against Thomas "Slab" Murphy is based on "utterly ludicrous" documentation which attempts to link him to a non-existent farming income, his defence barrister has said.