Work has already started on fitting out the 2,230 sq ft site, which could be open as early as next month.
The café will operate as a takeaway with seating available for customers to use after picking up their orders.
It will feature the Ridiculously Rich by Alana’s range of luxury cakes, other sweets including cookie pizzas and some savoury dishes including Reuben sandwiches with loaded fries.
Spencer is a self-taught chocolatier, initially running two shops in her hometown of Aberystwyth before setting up the tray bake-focused Narna’s in 2010.
In 2016 she appeared on BBC1’s The Apprentice and launched Ridiculously Rich by Alana following a £250,000 investment from Lord Sugar.
Alana opened the first By The Sea café in Aberystwyth in October 2020.
“After a successful six months at our first By The Sea concept store we decided it was time to expand,” says Spencer.
“Our key points to look for were beautiful waterfront spots that are on walking routes. Cardiff Bay ticked all these boxes for us.”
Other operators in the development - which is managed by Schroder UK Real Estate Fund - include The Cosy Club and Hub Box.