The Ronald Reagan Presidential Foundation had expressed outrage over the auction, in which bidding had reached over $30,000 (£19,000).
Guernsey-based PFC Auctions said in a statement that the vial would now be donated to the Reagan foundation.
The foundation said it was pleased the blood would stay “out of public hands”.
PFC Auctions, based on Guernsey in the British Channel Islands, said in a statement that the seller they were representing had bought the blood at a public auction in the US in February 2012 for $3,500.
The seller had now agreed for the item to be withdrawn from sale and donated to the foundation in “a considerable financial gesture”, it said.
According to the auctioneers, the seller is a “serious collector of presidential memorabilia” who did not think the Reagan foundation had any interest in the blood that he had bought.
The re-auction had “highlighted the importance of this historical artefact” the anonymous seller told them.
“I would personally be delighted to see this important artefact put on public display by the foundation”, the seller said.
The lot included a letter of provenance from the original seller who said their late mother worked at the laboratory which carried out blood testing for George Washington University Hospital after Mr Reagan was shot in 1981.
Mr Reagan, who went on to serve two terms as president, died at the age of 93 in 2004.
Mr Hinckley was found not guilty by reason of insanity and is being treated at a psychiatric hospital.