The 24-year-old spent two years with the Sky Blues following his move from Cambridge in the summer of 2007 and went on to make 28 starts, scoring seven goals.
Huddersfield chief executive Nigel Clibbens told his club's official website: "I can confirm we agreed terms with Coventry City on Monday for the transfer of Robbie Simpson.
"An offer of a three-year contract has been accepted following discussions and Robbie will join us after a medical and the paperwork is concluded.
"We don't usually comment on fees but we need to set the record straight this time. A fee has been agreed but the figures quoted in the media are off the mark.
"We are paying a fee now with some conditional payments which could be payable in the future."