The club submitted two applications to Erewash Borough Council to extend their facilities at Moor Farm.
Officers recommended the proposals be refused, but councillors chose to override their concerns and instead rubberstamped the plans.
The application will now go through due process before being sent to the Secretary of State for final approval.
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Club chief executive Sam Rush and academy manager Darren Wassall spoke at the borough council's planning meeting, with head coach Paul Clement and defender Richard Keogh also present alongside chief operating officer John Vicars.
Mr Rush said: "The training centre will be constructed to the highest possible standards and will be a legacy for both the local community and for the football club."
Concerns over the plans had been raised by nearby residents over traffic, the size of the buildings and the lack of public consultation.
Officers had also cited the fact the Moor Farm site was on green belt land, and the extension plans would therefore be "inappropriate".
Work on the training ground is expected to begin in the early part of next year.
Plans to expand Derby County Football Club's training centre have been unexpectedly granted.