In an opinion released Monday, the Connecticut Supreme Court unanimously said Brant was the owner of the 1962 silk screen that features 36 identical images of Elvis Presley's face.
Brant bought "Red Elvis" seven years ago from Lindholm's art dealer, who was later convicted of stealing it.
Brant, a longtime Warhol collector, paid $2.9 million to buy the painting while it was on exhibit in Europe.
In 2003, Swedish art dealer Anders Malmberg began serving a three-year term in Sweden on criminal theft charges in connection with the sale of "Red Elvis."
Lindholm had filed a civil suit alleging that Brant and Malmberg conspired to buy the painting without her permission.
But Superior Court Judge Chase Rogers ruled in 2005 that Brant made a reasonable effort to confirm that Malmberg was authorized to sell the painting.
The Supreme Court agreed, noting that Brant hired an attorney to conduct an investigation and insisted on a formal contract.