Sumo's shareholders will receive 513p in cash per share. The offer is at a 43 per cent premium to Sumo's last closing price of 358p.
Sumo's shares have risen sharply since its listing on AIM in 2017 at 100p.
Tencent already has an 8.75 per cent stake in Sumo and is the second biggest shareholder in the company, which has 14 studios in five countries with more than 1,200 employees.
Sumo's non-executive chairman, Ian Livingstone, said: "The board of Sumo firmly believes the business will benefit from Tencent's broad videogaming eco-system, proven industry expertise and its strategic resources, which will help secure and further the aspirations and long-term success of Sumo.
"The Board of Sumo considers that the acquisition is in the best interests of all stakeholders in the company and intends to unanimously recommend this offer to shareholders.
"Tencent’s offer of 513p per share demonstrates the tremendous achievements of the management team, both financial and operational, since Sumo joined AIM in December 2017 at 100p per share, and provides an outstanding return for shareholders.”
Carl Cavers, chief executive of Sumo, added: “In the 18 years since we founded Sumo, we have developed more great games than we could ever have imagined and enjoyed incredible trust and support from our clients, enabling us to grow into a global business, delivering consistently strong financial results.
"From a single studio in Sheffield, Sumo now totals 14 studios in five countries, spread across the globe, with more than 1,200 people. Sumo is and always has been a people business and great people make great games and enjoy great times. I am proud to lead such a talented and creative group of individuals.
"The three founders of Sumo, who work in the business, Paul Porter, Darren Mills and I are passionate about what we do and are fully committed to continuing in our roles.
"The opportunity to work with Tencent is one we just couldn’t miss. It would bring another dimension to Sumo, presenting opportunities for us to truly stamp our mark on this amazing industry, in ways which have previously been out-of-reach.
"Tencent has a strong track record for backing management teams and their existing strategies. Alongside the acceleration of Own-IP work, Tencent has demonstrated its commitment to backing our client work and has stated its intention to ensure that we have the necessary investment to continue focusing on work with our key strategic partners on turn-key and co-development projects.
"We love what we do and have some amazing relationships with the world’s best videogames publishers. Sumo will continue to work with these clients to break new ground and create even more fantastic games. We look forward to strengthening our growth prospects through the application of Tencent’s strategic resources to our Own-IP, turn-key development work ambitions, and possible acquisition opportunities.
"We believe that the acquisition is in the best interests of everyone connected to the business - our shareholders, our people, and our clients - and thank all our stakeholders, past and present, for the resounding support they have given us over the years.
"The future for Sumo is more exciting than ever.”