Former Arsenal man Ayto is on board with immediate effect following the departure of David Weir.
Cave, who was assistant to Weir, now steps up as technical director.
Deputy chairman and chief executive Paul Barber said: “We are delighted to welcome Jason to the club. We are all very much looking forward to working with one of the most talented young sporting directors in the country.”
Ayto, 40, will report to Barber and work closely with men's and women's team head coaches Fabian Hurzeler and Dario Vidosic.
He will also oversee all footballing areas of the club, including player recruitment, performance and medical for the club’s senior men’s and women’s teams and academies.
In the club announcement, Ayto said: “I’m honoured to be appointed sporting director at Brighton and Hove Albion and I’m very grateful to Tony Bloom, Paul Barber and the board for this opportunity.
“This is a special club, admired across the footballing world for its culture, ambition and smart thinking, all of which has underpinned some remarkable progress in recent years.
Cave joined Albion in November 2022 from Fulham.
Reporting to Ayto, he will take on responsibility for the men’s and women’s teams, the club’s academies and day-to-day management of the men’s first team technical departments.
Barber said: “Mike’s work since joining us three years ago has been hugely impressive, and I have been delighted at the impact he has made across our technical areas.
“Mike fully deserves this promotion, and I would like to congratulate him on his new role.”
Cave, who graduated from Loughborough University with a degree and masters in Sports Science and Sports Management, said: “I’d like to firstly thank Tony Bloom and Paul Barber for their continued support during my time at Brighton.
“I’d also like to put on record my thanks to David Weir for the opportunity and support he’s shown me since I joined.
“Having this new opportunity to further grow my role and involvement at the club is an exciting next chapter for me personally.
“Having the chance to take on this role working alongside Jason is something I’m extremely excited about. Jason’s reputation amongst his peers and within the wider game is outstanding.
“We have complimentary skills and experiences that I believe will allow us to continue to innovate and develop our technical areas towards our goals as a club.”