The BBC drama features the stories of a US prisoner on death row, a vicar in an English village, and a maths teacher trapped in a cellar.
The four-part mini series will show them crossing paths in an unexpected way.
The Devil Wears Prada star Stanley Tucci has also been cast, alongside Dracula's Dolly Wells.
Inside Man, which is also being produced for Netflix, was created and written by Doctor Who and Sherlock writer Steven Moffat and his wife Sue Vertue, who will also be an executive producer on the show.
"We're a bit stunned, and very excited, at the acting talent we're managing to assemble for this show," they said in a statement. "Can't wait to crawl out of our lockdown bunker and get to work."
Chris Sussman from Netflix added: "We're delighted to team up with the BBC on another brilliant series from the ingenious mind of Steven Moffat.
"It's impossible to say too much about Inside Man without giving away spoilers – so let's just say the scripts are fiendishly clever, the cast is fantastic and at this point in time nobody but Steven knows how it's going to end.
"We're thrilled to continue our fruitful partnership with BBC One, BBC Studios and Hartswood Films and are excited about bringing this series to a global audience."
Filming will start later this and the show will air on BBC One and BBC iPlayer in the UK, and on Netflix outside of the UK and Ireland.
West received a lot of praise for her role as Jill Baxter in Russell T Davies' groundbreaking drama It's a Sin.
"What's interesting is that sex at the time was so liberating and so fun and people were living their truth, having sex and having a great time," Lydia told the Make It Reign podcast.
"I think it just shows just how much work there is still to do on banishing homophobia, transphobia, biphobia that's out there. There's still just so much work to be done. That is very much the jobs of allies to do."
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