Crime follows the story of Detective Inspector Ray Lennox who is put onto the case of a missing schoolgirl, and during the six-part series delves into his troubled mind and the battle with his own demons.
"It couldn't have worked on traditional TV, it couldn't have worked on terrestrial TV, we couldn't really make the show we wanted to make," said Welsh, who wrote the novel the new series is based on.
"We were still until fairly recently stuck in these, sort of, dark ages of everything has to be BBC, ITV, Channel Four. And we have got platforms now that we can do things in a different way. I think it opens up drama, I think drama in this country, TV drama, will come of age now," he said.
He said the "luxury" of the streaming platform meant it could get into the character driven drama much more quickly than programmes like Line of Duty.
The series is based on Welsh's 2008 novel of the same name, which sees DI Lennox jet off to Florida with his girlfriend Trudi Lowe, played by Angela, to try and recover from the breakdown suffered in Edinburgh.
In the book the parts featuring the Edinburgh were just a "small chunk" of the story, said Welsh, "so it was like adapting something but it's also like writing the original thing because we had to fill so many gaps and we had to do so much with the characters."
Dougray Scott, who stars as the rouge detective, said Welsh and his co-writer Dean Cavanagh "expanded, focused, imagined a lot of the story in Edinburgh".
DI Lennox battles with addiction problems in the series, while deploying unorthodox tactics while investigating the disappearance of the missing schoolgirl and the link to a serial killer.E
Welsh described the detective inspector as a "compulsive obsessive hunter for the truth" who "doesn't recognise the realpolitik of the criminal justice system".
"He believes that law's for everyone and he believes that violent and sexual crimes against the person are the real kind of heinous crimes and the rest are kind of just misdemeanours."
He said the lead character, in taking the "disturbed and dangerous people" outside of the game, was a way to cleanse and purify himself from his past experiences.
"He's not really concerned about the machinations of law, the legal system, or what's on the statute book. He just wants to stop bad people doing things to ordinary citizens. And I think the reason he wants to do that is because he's just in this massive flux about himself."
And on playing the troubled character, Scott said: "It became very personal for me and he really felt like it was part of me towards the end, and it's exhausting".
"It's not something that you can easily step out of when you go home at night, it's kind of constantly with you."
Filmed in Scotland's capital and Glasgow, Crime also stars Joanna Vanderham, Ken Stott, and Jamie Sives. The programme will be available on streaming service BritBox on Thursday.