The free app includes a series of games and problem solving activities that are designed to help people understand and develop their cognitive skills.
The company said it will work with experts from Cambridge University, IntelliGym (ACE), Brainways and C8 Sciences to develop new programs.
These "premium" products will focus on a specific cognitive performance skill, such as attention span, decision-making, working memory and creative thinking. They will be marketed as advanced training courses and they'll cost users an average of $20 (£13) each.
"Partnering with institutions like Cambridge University and C8 Sciences represents the first opportunity for leading neuroscientists to bring tried-and-tested brain training solutions to millions of Peak users around the world," said Peak cofounder and CEO Itamar Lesuisse.
"By opening our platform, we are providing access to globally recognised brain training solutions from the best scientists in their field."
By way of example, C8 Sciences will provide Peak users with an attention-training program that features 1,000 minutes of play over 12 weeks.
Peaks is also giving partners access to data so they can research and track the impact of their programs, run efficacy tests and potentially publish their findings.
Professor Barbara Sahakian, a clinical neuropsychology professor at the University of Cambridge, said the partnership with Peak will bring the games industry to a new level and promote the benefits of cognitive enhancement.
Peak is currently available on iOS, Android and Kindle but the advanced training courses will initially only be available on iOS, when they go live on 28 May.