Officials hope to eventually use the bison to establish new herds on public lands. But conservationists see the move as privatizing Montana wildlife.
The bison have been held in federal quarantine for the past several years to make sure they don't have the animal disease brucellosis.
Turner offered to hold them for five years — the duration of the quarantine program — in exchange for keeping 90 percent of their offspring. That could amount to about 190 animals to offset his costs.
The U.S. Department of Agriculture, which runs the quarantine in Corwin Springs, Mont., also opposes the move.
Bison, or buffalo, once numbered in the millions across North America but were driven to near extinction.
Turner Enterprises general manager Russell Miller said Ted Turner stepped in after Montana Gov. Brian Schweitzer asked if he would consider submitting a proposal for the animals.
Turner wanted to help the state after prior efforts to relocate the Yellowstone bison had failed, Miller said.
"I see this as a perfect blend between conservation for the public good and privatization to recoup the costs," Miller said.
It would cost about $480,000 to tend to the animals over the five years, he said.
Ken McDonald with Montana Fish Wildlife and Parks said the animals could be moved to Turner's sprawling Flying D Ranch by late February.
An environmental study must be done first, then the department would open the plan to comment for 30 days.
Officials recommended the moved last month. Final approval must be given by Fish Wildlife and Parks chief Joe Maurier.
Turner already owns about 50,000 bison, most domesticated, on ranches throughout the West. His restaurant chain Ted's Montana Grill serves buffalo burgers, although Miller has said the Yellowstone bison are prized for their pure genetics, not their meat.
The animals would be kept on a 12,000-acre parcel within the billionaire's 113,000-acre ranch south of Bozeman.
State officials were initially reluctant to put the animals on private land. But McDonald said the bison faced possible slaughter if no home was found.
"They need to get moved out of that facility," he said.
Fourteen more of the animals would be shipped to Guernsey State Park in southeastern Wyoming and kept on about 1,500 acres, said state park administrator Dominic Bravo. He said their offspring could be distributed to other state parks or interested public landowners.
"For us, the opportunity to have Yellowstone's pure genetics would be great," Bravo said. He said the herd would likely double in size over the next five years.
The bison have been tested extensively for brucellosis, a disease carried by many of Yellowstone's wildlife that can be transmitted to cattle and cause premature abortions.
Fears over the disease helped sink an earlier attempt to move the quarantined animals to Wyoming's Wind River Indian Reservation.