Rotherham had played at Millmoor since 1907, while the Don Valley Stadium is already home to the Sheffield Eagles rugby league club, as well as being a major athletics venue.
"It was the only option left open to us," Rotherham chief operating officer Paul Douglas told BBC Look North.
"We tried long and hard to negotiate terms that would allow us to stay - unfortunately those talks broke down, and we've had to move away.
"We needed to settle a lease to allow us to stay here and be a financially viable club, and we couldn't do that."
The Millers have been in administration since March, when they were handed a mandatory 10-point deduction by the Football League.
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