The 26-year-old is out of contract and Rangers were only prepared to offer £20,000-a-week for a new deal.
Reports claim Birmingham are leading the chase for Boyd.
“Kris is going,” Smith told the Daily Record. “There is no doubt about that now.
“We have never wanted to admit he would leave but we are doing so now.
“We’ve made him an offer but he’s getting much higher offers from other clubs and he is going.
“Kris leaves here with the best wishes of every one of us at Rangers. He has been absolutely terrific for this club and his scoring record is second to none.
“I know people have said I had a problem with Kris because I left him out of a lot of my starting teams but I actually get on very well with him. I must admit I like him and I hope he is a success wherever he goes.
“I’m disappointed we can’t offer enough to keep him with us but I really do wish him continued success.”