Smith has given up hope of the club's star striker signing a new contract at Ibrox and wished him well at which ever team he ends up joining.
Boyd, whose 26 goals last season helped him become the Scottish Premier League's all-time record scorer, has been linked with Birmingham, Newcastle and Turkish outfits Kayserispor and Trabzonspor.
Smith, who this week signed a new one-year contract himself, told the Daily Record: "Kris is going. 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."
Boyd will join Nacho Novo, DaMarcus Beasley and Steve Smith in leaving Rangers when his contract expires.
Captain David Weir and Kirk Broadfoot have also yet to agree new deals, while Danny Wilson, Kevin Thomson and Madjid Bougherra have all been linked with moves away.
Smith admitted he would start next season with a smaller squad than the one just gone but is confident debt-laden Rangers will be able to buy players for the first time in almost two years.
However, he has warned they are unlikely to be of a standard to improve the club's fortunes on the European stage.
He said: "It's obvious we'll need players for every department but we've got to face up to reality. We'll make every effort to improve the squad but can't kid people on that the Champions League arena will be one in which we will excel.
"We'd need to have some exceptional players to do that but we'll have a smaller squad augmented by some younger players who I'm hoping are ready to make their challenges. Obviously, it will be tough for us but this club has met challenges before.
"We've been looking for players although financial restrictions make it difficult to get the right type. But I must admit our position with the bank is far clearer than it has been for a while.
"For the first time, (chief executive) Martin Bain and myself have direct contact with the bank and there's a better understanding on both sides of what is required. But the bank is now more appreciative of what Rangers, as a team, need."
Smith revealed he had made up his mind to quit at the end of the season before having a change of heart.
He said: "I was in a situation where the club had been up for sale for the majority of the three-and-a-half years I'd been there and I just thought it was right for me to get out.
"I had already emptied my office. I wasn't going back but when the dust had settled and I'd had time to sit down and reflect on everything a few things kept forcing themselves to the front of my mind.
"For instance, I realised the situation at the club was poorer now than it had been a year previously when I'd originally thought about finishing up. I had to ask myself if I could walk away under such circumstances."