"We are happy to provide our stadium for their use for as long as it is needed. It is an exciting time for both us and Rotherham United," Smith told HRMedia.
The stadium, which is part of the Sheffield International Venues company, will provide the Millers with an 8,000-seater main stand that will include a director's box, press box, an official Rotherham United store and a large concourse area.
The club will also have access to a coaching area and treatment room, the first aid room, the board room and VIP lounge and Smith believes that the stadium will have no problems coping and hopes that the club will have a successful time in Sheffield.
"We have a fantastic track record at staging major events and in the past we have hosted both Sheffield United and Rotherham reserves games, the Chengdu Blades and junior international football, so staging League Two fixtures won't be a problem.
"We hope Don Valley will prove to be a successful home for the Millers, until they can move back to Rotherham, and we look forward to seeing them recording a win against Lincoln City when the new season kicks off in August," added Smith.