The pair are the second set of captains to be announced for the tournament, following Aaron Finch and Lauren Winfield (Northern Superchargers).
Knight, who captained Western Storm to this season's Kia Super League title, will be reunited with the man who coached them to that success, Trevor Griffin. Lisa Keightley, the former Australia international, had been due to coach Spirit in the competition, but her appointment as England head coach opened up the opportunity for Griffin - who is currently Sydney Thunder's coach in the WBBL - to take over.
"I'm really looking forward to captaining the London Spirit women's team in The Hundred next year," said Knight. "With the new format there's going to be the chance to have a real tactical input as a captain and I'm excited to work that out and also bring together a new team in a new competition.
"It's also brilliant that Trevor has been announced as coach, I really enjoyed working with him in the KSL and hopefully we can have more success together.
"Our team is now really beginning to take shape, having also recently signed Deandra Dottin. I'm looking forward to working with her, Trevor and the rest of the squad once they're confirmed."
Griffin said it was "an honour" to be appointed head coach.
"I am thrilled to announce Heather as our captain," he said. "She is a brilliant cricketer and a natural leader with significant experience in captaining sides. I'm really looking forward to being involved with The Hundred and contributing to this next big step in the development of the professional women's game."
Morgan, whose captaincy experience includes 44 T20Is leading England and 33 games as Middlesex skipper, said: "I can't wait to get started as captain of the London Spirit men's team. It's going to be a hugely exciting new competition and I'm looking forward to being a part of it.
"The draft went fantastically well for us and we have an outstanding squad with the likes of Mark Wood, Mohammad Nabi and Dan Lawrence in our team.
"As a player and a captain I am always looking for ways to improve and it's clear from speaking to Shane - who has an amazing cricket brain, about everything from tactics in this new competition to how to get the best from our squad - that this is an exciting opportunity to take cricket forward."
Shane Warne said he was "over the moon" to have Morgan confirmed as captain. "He has had a truly unforgettable year and we all know that he is an outstanding leader," said Warne. "I believe he can give our team the edge in The Hundred."