Ms McAlpine, who married Gray in 1991, passed away after a short illness last week.
Gray said that his wife, who had once published his poems in her own imprint, had "done much to hide the fact that she was ill" and was only recently hospitalised.
A private funeral will be held in Cardross.
"We had our 23rd wedding anniversary recently and we had been living together a year before we were married," he said.
"I had left several works of art to her in my will, but now I will be offering them to Glasgow art galleries in her name, if they will accept them."
He added: "She will be buried. There's nothing that can go wrong which already hasn't."
Ms McAlpine frequently accompanied Gray to his many literary events, and was known to counsel the artist and writer on his work.
The couple met in the Ubiquitous Chip, the Glasgow restaurant which houses one of Gray's most famous murals. Ms McAlpine, who was 64, was a bookseller and also once set crosswords for The Lennox Herald.
Gray's first wife and the mother of his son, Inge Sorensen, died in 2000.
A spokesman for Cargo, which published Gray's, Of Me and Others, said: "Over the course of our association with Alasdair, we got to know Morag well and we are deeply saddened by her passing.
"We remember her tremendous spirit, her warmth and her passion; all our thoughts are with Alasdair at this difficult time."
In an interview with The Herald published 10 years ago, the couple spoke of their similarities, with Ms McAlpine saying: "I think that we probably had quite lonely times before we met. And we now know the value of being together."