Called Terra Carta Design Lab, the project "will invite some of the world's most talented design students to design high-impact, low-cost solutions for nature, people and planet".
It was launched on Saturday to mark 100 days to go until the COP26 climate conference.
Students and recent alumni of the Royal College of Art in London will be invited to form teams to submit proposals that will help improve biodiversity, tackle greenhouse gas emissions and develop new social and economic models.
"I'm incredibly proud to be part of the Terra Carta Design Lab founded by His Royal Highness The Prince of Wales," said Ive, who left Apple in 2019 to start San Fransisco design studio LoveFrom.
"It's a visionary and imaginative way of helping address the world's increasingly urgent environmental problems," added the former vice president of industrial design at Apple, who was appointed chancellor of the London post-graduate art school in 2017.
"Often the biggest challenges demand the most ingenious, most creative thinking, which is why I'm so excited about the work that the RCA students will be able to contribute through this collaboration. I know that their creativity and inventiveness will develop truly powerful solutions."
Shortlist will be announced during COP26
The project will seek concepts that demonstrate how design, the arts, science and engineering can contribute to finding solutions to climate change.
A shortlist of the best ideas will be announced during COP26 in November and a winner will be announced in 2022.
"Small ideas can have a big impact if they are supported with the right design, science and engineering and that is the key idea behind today's Terra Carta Design Lab," said The Prince of Wales.
"We only have 100 days until COP26, the big UN conference in Glasgow to tackle the climate and biodiversity crisis, and we will all need to play our part, old and young, if we are to change how we look after the Earth, making it sustainable for nature, people and planet."
Prince Charles launched Terra Carta initiative earlier this year
Terra Carta Design Lab is a branch of Terra Carta, an initiative launched by Prince Charles earlier this year to provide "a practical roadmap for acceleration towards an ambitious and sustainable future".
Terra Carta is in turn part of Sustainable Markets, a project the prince launched in 2019 to help encourage private-sector solutions to the world's problems.
Other projects that will be shown at COP26 in November include a pavilion that will showcase solutions to the built environment's carbon emissions. The UK Green Building Council is currently looking for "playful interventions" that convey the scale of the sector's emissions.