The Portuguese winger has been at the centre of transfer speculation this summer with an expectation he would move on from Vitoria Guimaraes.
West Ham have been heavily linked with Silva as they look for extra options in the final third and they were even claimed to be leading the race.
He is now flying to England as Forest look to put him through his medical paces and finalise the deal.
Nottingham Forest will pay an initial €7m for Silva, with a further €5m in add-ons dependent upon how he performs at the City Ground and how many appearances he makes.
Silva found the back of the net on 15 occasions for Vitoria over the course of last season.
Nottingham Forest will be hoping the Portuguese can hit the ground running under countryman Nuno next season.