Lewis, who was Head of Commercial at Sheffield United until his departure at the end of August, is set for a role reversal with Coakley who heads to Bramall Lane shortly to take up a new challenge.
The Millers confirmed Coakley's departure last month after his oversight into much of the commercial work for the new stadium project.
It is unclear as yet if Lewis will take up a seat on the clubs board of directors.
This latest appointment will add to the arrivial of the Millers new Head of Community, Jamie Noble.