Simpson joined City from Cambridge United two years ago and scored seven goals in 28 starts plus 43 substitute appearances.
"I can confirm we agreed terms with Coventry City on Monday for the transfer of Robbie Simpson," Huddersfield CEO Nigel Clibbens told his club's official website.
"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."