McKay has scored 22 goals this season and manager Terry Butcher was delighted to tie down the 24-year-old, who added a one-year extension to his current deal which has a year to run.
Draper has been a regular starter for Inverness this season and his fine form has earned a fresh one-year contract.
Butcher said: "Billy's been phenomenal this season, surpassing Craig Dargo's club scoring record with 11 games to spare.
"Apart from his goalscoring flair, Billy is a very popular and much-prized asset to this club.
"He's attracted attention with his goals but he loves Inverness, he's happy at the club and he had no hesitation in putting pen to paper.
"Ross has established himself with us as an extremely professional and powerful midfielder who can both score goals and create them.
"He's good at set pieces and his physical presence in the penalty area has been an advantage. Ross and Owain Tudur Jones have formed a fantastic barrier in front of our back four. We're delighted he will be staying with us next season."
McKay told the club's website: "Coming to Caley Jags has been a great move for me and now that the deal is signed, it gives me continuity and I can focus on the team achieving the best SPL finish we can."