The all-Australian consortium BBHO withdrew its planned $386 million proposal on Friday.
"We congratulate the Hancock Shanghai CRED consortium for similarly recognising the potential of the iconic Kidman brand," it said in a statement.
The decision by BBHO came after the Kidman board unanimously recommended the Hancock Group-Shanghai CRED's $386.5 million offer made on Wednesday.
"We are disciplined investors in Australian rural assets and made what we believed to be a full and fair offer," BBHO said.
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The consortium thanked the public, "all off whom recognise the importance of the Kidman name and legacy", for their support and good wishes during the bidding process.
BBHO, made up of the Buntine, Brinkworth, Harris and Oldfield grazier families, also wished Ms Rinehart and her Chinese partner well.
"Should they be successful in completing the acquisition, we look forward to welcoming them as neighbours."
S Kidman and Co is Australia's largest private landholder.
It comprises 100,000 square kilometres of pastoral leases and 185,000 head of cattle in Western Australia, South Australia, Queensland and the Northern Territory,
The winning consortium will need Foreign Investment Review Board approval.
However, Ms Rinehart says she's prepared to go it alone if her Chinese partners are knocked back.
Treasurer Scott Morrison has already twice rejected sales of Kidman.
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