Revell, 31, spent three-and-a-half seasons at the New York Stadium, elevating himself to cult status with his double in the League One play-off final against Leyton Orient last May.
But with his contract due to expire in the summer, he has opted to join Cardiff on a two-and-a-half-year deal.
“All we can do is wish Alex well,” said Raynor. “Talks have been ongoing with Alex and his representatives since the summer and they just couldn’t get it over the line.
“When you’ve got an asset like that who is intimating that he isn’t going to sign then when a bid comes in from Cardiff, who met our valuation after we rejected their initial bid, then all you can do is give them permission.
“And Alex has decided his future lies with Cardiff City. We wish him well, he’s been an absolutely fantastic servent for Rotherham United.
“I won’t forget his heroics at Wembley and I’m sure Rotherham fans won’t either. He’s gone down in the club’s history, but players move on.”
In what has been a busy first week of the transfer window, Rotherham have signed Adam Hammill and Danny Ward on loan from Huddersfield, with a permanent deal for the latter expected to be concluded early next week. They have also signed Jack Barmby on loan from Leicester.
“They’re players we feel can give us a real goal threat, which is something we’ve lacked,” added Rayner.
Rotherham also accepted an offer from Millwall for midfielder Ben Pringle, although the player could not agree terms. Fabien Brandy and Michael Tidser have had their contracts terminated.