The couple were together 59 years. They got married aged just 16 having grown up in south Wales.
Speaking to RTÉ, Jones said that that he and Linda had "known one another since we were kids", adding that she "knew me very well".
Tom Jones also spoke about the moment he found out about his wife's illness and how she encouraged him to keeping performing.
"She told me, she knew she had lung cancer, and we talked about it, and I thought that I was going to fall and she said 'you can't fall with me, you've got to carry on, because you won't be able to live unless you sing, I know that", Jones said. "That's really what she told me not to do and that's why I'm singing this song, this is for her".
That track from the album is called "I Won't Crumble" and you can check it out below.
Tom Jones even revealed that he visited a therapist following Linda's passing. "First of all I had to go and see a therapist in Los Angeles, a grief therapist and she said 'your wife wants you to carry on', and I said 'yes, she does", he said.
Jones added that the therapist had asked him what would be the most difficult song for him so sing from the album, to which he had replied Bob Dylan's, "What Good Am I?". Tom Jones explained that the song is about "a person standing by while something happens to somebody else". He said that this "really hits a sore spot" for him.
The therapist encouraged him to sing that song first and if he came through it, then he was on "the road to recovery".
"So I did", Jones said. "I got a few musicians together and I tried a few other things first and then I tried that one and then we went to Hampton Court in the same year to start a tour".
"That first show the audience was aware that I was under pressure and then you realise that the audience really lifts you up", he added.
"After that first show I realised that I could do it and the audience are there with you, and that's a big deal. It opened my eyes, I thought 'well this is going to save me' as opposed to hurt me, it's going to lift me up. And that's what's happened".
Jones said that he hopes to return to touring by mid-July. "I can't wait to get back to doing live shows because that's where I live really, on the stage", he said.
