The-21-year-old has made 15 appearances for the League One outfit since joining on loan in November.
The full-back has now signed a two-and-a-half year contract with Coventry, and manager Mark Robins said: "I am delighted to secure a player of Blair's potential for Coventry City Football Club.
"He has proven capable of playing at a consistent level and he will, I am sure, be an asset to us.
"He also has the personal qualities I am looking for in players I recruit. He is professional and determined to succeed and we welcome him to Coventry City on a permanent contract."
Adams is the third player to commit to Coventry in the January transfer window after Leon Clarke agreed a two-and-a-half year deal, while Franck Moussa signed an 18-month contract.