Londoner Grabban was expected to sign for Crawley after the two clubs agreed a transfer fee earlier this week, but prolonged talks with the newly-promoted club have broken down and the 24-year-old, who has a year left to run on his current deal, will stay with Rotherham for their first season at New York Stadium.
Millers manager Steve Evans said: "Lewis is a top class footballer and for that reason alone I'm delighted he remains a Rotherham United player.
"There has been significant interest in the player, but to date only Crawley Town have agreed to meet the valuation I placed on the player on my arrival at the football club.
"Only Lewis himself or Crawley Town can turn the tap on which has in the last couple of hours been turned off."
Meanwhile, defender Michael Raynes, who was made available for transfer by Evans, has left the club by mutual consent.