Liverpool Mayor Joe Anderson said it was a great deal for taxpayers, with the club paying about Â£4.4m per year in return for the council's support.
But the city's Liberal Democrat leader Richard Kemp asked why a club largely owned by "billionaire" businessman Farhad Moshiri needed council backing.
He asked: "What are the safeguards?"
The council cabinet has agreed to set up a Special Purpose Vehicle (SPV) to help Everton secure the investment it needs to build a new 50,000 capacity ground at Bramley-Moore Dock on the banks of the Mersey.
Everton last week announced a deal to acquire the land needed for the project.
The local authority said its agreement with Everton includes measures to ensure it will always be paid by the football club.
"It is not just a good deal for the council in terms of receiving funding but equally it is going to be the driver for regeneration for north Liverpool," said Mr Anderson.
"From my point of view, it is job done."
Mr Kemp said he still has his doubts.
"I am not against the deal itself but I want to know what the safeguards are. I want to know the direct benefit for the council.
"Why do billionaires need a guarantee from a third party? In fact why do they need a loan at all?"
Mr Anderson said he had had several meetings with Iranian businessman Mr Moshiri, who bought a 49.9% share in the Premier League club last year.
"We're not funding a billionaire - we are actually doing a great deal for Liverpool City Council," said Mr Anderson.
"I am not here to browbeat Everton into starting but... I certainly want them to crack on because if we get chosen for the Commonwealth Games in 2022 we will need to deliver."
Prof Tom Cannon, emeritus professor at the University of Liverpool's School of Management, said the stadium would bring direct benefits to the city and the council.
"The economic benefit is development of another strong economic agent in a growth area like sport and it reinforces the city's burgeoning strength as a leading centre for an array of sports from soccer, through equine to golf.
"Sport is a high-growth industry with strong multipliers."
Everton Stadium deal

The Public Prosecution Service (PPS) said Mr Wells would not be charged in connection with the incident on 23 April in Downpatrick.
Mr Wells welcomed the decision as "an important step forward".
In a statement, the PPS said it was decided that the case did not meet the test for prosecution.
"Following a careful consideration of all the available evidence provided to the PPS by the PSNI, it has been decided that the case does not meet the test for prosecution," the PPS statement said.
"Potential offences were considered under the Public Order (NI) Order 1987, in particular an offence under article nine (stirring up hatred).
"Included in the evidence examined by prosecutors was a 30 second video clip which was widely circulated on social media after the event was staged in Downpatrick.
"The police also provided a longer transcript of a recording of the entirety of the man's comments.
"On examining the available evidence for the incident reported, in particular the entirety of the transcript of the man's comments, it was concluded that there was insufficient evidence to prove that any offence was committed."
In a statement, Mr Wells said he had been "vindicated" by the decision.
"This matter has been hanging over me for some time and so I am obviously delighted to have the air cleared," he said.
"It was seized upon by opponents of myself and my party and used against us in an entirely unreasonable manner.
"There are many aspects of this incident, and the subsequent campaign, that continue to raise significant cause for concern and which merit further investigation."
Everton's ambition to build a new Â£300m stadium has been backed by Liverpool City Council, which has formally agreed to financially guarantee the project.
[NEXT_CONCEPT]
The DUP MLA Jim Wells will not be prosecuted for comments he made about gay marriage during a hustings event for the Westminster election.