Calderwood flew back from Dubai to speaking to the Forest Chairman and has signed a 3 year deal with the Midlands club.
The 40 year old who has three seasons managerial experience with Northampton, including promotion in 2005/2006 made it through to Town's shortlist for Royle's successor and was widely regarded to be the favourite in the later stages.
Town may now decide to approach Carlisle United to ask permission to speak to promising manager Simpson.