His comments follow the announcement of a £620 million financing to support projects and UK exports to Africa.
The prime minister said he aims to "attract the best talent from around the world, wherever they may be" by creating a system that is "fairer and more equal."
Johnson was setting out his vision of Britain after Brexit to the UK-Africa Investment Summit in London, as he pitched for improved business links with Africa.
And - at the summit also attended by the Duke of Sussex - the PM also announced an end to UK support for thermal coal mining or coal power plants overseas in a bid to use trade to tackle the climate crisis.
The new £620m funding will be used to support infrastructure projects including financing hospital beds and healthcare centres in Ghana and Zambia, a business park in Uganda and road upgrades in Gabon, International Trade Secretary Liz Truss said.
Truss told the summit: "Africa is home to eight of the 15 fastest growing economies in the world and its economic prosperity matters to the UK.
"We want the UK to be the partner of choice in Africa so I am delighted that with UKEF's support, British expertise will form a key component of these infrastructure projects that will directly improve millions of lives.
"We are committed to strengthening our trading relationships in the region, to help deliver jobs and economic growth that will benefit African and British businesses alike."
The funding comes as UK Export Finance (UKEF), which helps UK businesses win contracts and financial support overseas, provided almost £2 billion of support in the last two years.
The secretary’s comments were echoed by the prime minister, who declared: "We want to be with you, side by side, every step of the way."
"Together, let us write the next chapter for your country, for my country, and above all, for all the peoples of our countries," he added, as he welcomed the delegation to London.
The call for African talent to come to the UK signals, as ITV News political correspondent Paul Brand says, that Johnson's "instincts are relatively liberal on immigration."
His comments also reveal a desire to extend Britain's influence across the globe.
"Africa is the future," he told the delegation, "and the UK has a huge and active role to play in that future."
"We are and we will be your partner through thick and thin."
Some of the main projects supported by the fund, which is overseen by the Department of International Trade, include a project for Ghana worth £110 million for Contracta Construction UK which will upgrade Kumasi teaching hospital, creating 750 beds for maternity care.
There is also £40 million worth of support to enable the further development of Kumasi Airport, improving transport links for tourist and commercial use - increasing capacity by an extra one million passengers a year.
For Zambia, a direct loan of £244 million is being lined up for 108 rural healthcare clinics - powered by solar energy - and three hospitals by NMS Limited.