Test fixtures at Yorkshire's headquarters from 2020 onwards appeared to be in serious doubt after it emerged last week that the council had withdrawn a £4million grant to help fund necessary refurbishment to the stand at the Football Ground End.
That work was required in order to achieve minimum capacity requirements stipulated by the England and Wales Cricket Board.
But Yorkshire confirmed in a club statement on Tuesday lunchtime that a favourable new deal has been agreed.
Club chief executive Mark Arthur welcomed the financial arrangement, supported by the council and under which work should now begin on the stand at the end of this summer.
"We would like to thank Councillor Judith Blake and Leeds City Council for their support in reaching this point," he said.
"There is still a long way to go - however, it is a significant step in securing the future of international cricket at Headingley.
"Yorkshire County Cricket Club will continue to work hard to ensure that all remaining funds are in place to ensure that the redevelopment is completed in time for the Cricket World Cup in 2019."
Reports indicate a £35million deal has been struck with a London-based investment company.
Yorkshire declined to cite specific figures or the identity of any new partners, referring only to "an agreement with a financial institution".
The club said: "The Yorkshire County Cricket Club have welcomed news that a funding agreement for the redevelopment of the North-South Stand at Headingley has been supported in principle by Leeds City Council, subject to approval at executive board (level).
"This news comes after Leeds City Council gave their support in principle to Yorkshire County Cricket Club in reaching an agreement with a financial institution for a funding arrangement to support the redevelopment."
Further details are expected to appear in the council's executive report when it is published next week.
There had been worries, voiced by Yorkshire chairman Steve Denison, that Headingley might initially lose fixtures previously granted during the 2019 World Cup and then fail to meet requirements to be considered to stage Tests from the following year - and perhaps even miss the opportunity to host one of the eight teams set to take part in the ECB's planned new city-based Twenty20 tournament from 2020.
Those concerns have apparently been short-lived, however.
