The initiative was launched last July by Hamilton and his Mercedes team, and is co-ordinated by his Mission 44 charitable foundation.
The first recipients are Motorsport UK and the Royal Academy of Engineering, who will receive over £500,000 from an initial total of £5 million of seed funding.
The Motorsport UK programme is focussed on increasing female participation in grass roots motorsport via the FIA Girls on Track initiative, which has been running since 2016.
It now has a focus on "developing new partnerships to reach more communities with high representation from low-income and minority ethnic groups".
The Royal Academy of Engineering programme will back Masters-level motorsport engineering scholarships for Black students, and will support at least 10 successful candidates on MSc courses across the 2023-24 and 2024-25 academic years, selecting five each year from final year undergraduates.
Hamilton made it clear that the first grants are just the start of a long-term programme, while highlighting the context of recent controversies involving Nelson Piquet and Juri Vips.
"I'm very proud to see Ignite announcing our first two grants today," he said. "There has been a lot of work behind the scenes since launching and I'm delighted that Mercedes and I can continue to demonstrate our commitment towards creating a more diverse industry in this way.
"We chose these grants because they focus on supporting individuals from two crucial and underrepresented demographics, moving us towards our goal of increasing the number of women and Black talent in the sport.
"The events of this week have shown us why there continues to be an urgent need to push for better representation in our industry.
"More than ever we must focus on how we can use action to change motorsport for the better and this is an exciting next step."
Mercedes boss Toto Wolff added: "These two grants demonstrate the wide range of opportunities that can make a meaningful contribution to the partnership's overall goal.
"From inspirational motorsport events and experiences that will show the power of possibility to thousands of girls and young women in the UK - to academic support for some of the brightest and best Black engineering students in the country - we intend for each initiative to make a tangible contribution to building a more diverse and inclusive motorsport industry."
