The deal is for 100 per cent of Climax Studios shares, of which Hyperion Capital Limited held 82.5 per cent.
Meanwhile, Climax Studios CEO Simon Gardner and James Sharman owned 15 per cent and 2.5 per cent of company stock.
"We are very excited about joining Keywords, and the opportunities that being part of an industry-leading global business will open up to our clients and our team," said Gardner.
"Keywords Studios shares our growth ambitions, and their investment will support the delivery of a wider range of top quality services and products to our clients.
"We are looking forward to working closely with everyone at Keywords and to start playing our part in the impressive journey of the wider business."
Since being founded in 1988, Climax has aided in the development of many games for various companies such as Microsoft, Electronic Arts, Sony and Codemasters.
Specific titles included Silent Hill: Shattered Memories, Crackdown 3 and the upcoming PS5 exclusive, Returnal.
Part of the family
Keywords will pay a maximum of £43 million ($60 million). However, this is subject to Climax hitting specific targets.
Initially, the agreement will see Keywords part with £20.2 million ($28.1 million) and £6.8 million ($9.4 million) worth of new ordinary shares.
Up to £16 million ($22.5 million) will be paid based on performance over the coming year.
Climax Studios was a natural acquisition for Keywords Studios, given the company provides games development services, intending to be the 'go to' tech service platform.
"We are delighted that Simon and the highly talented Climax team are joining the Keywords family," said Keywords Studios interim CEO Jon Hauck.
"Climax brings a wealth of expertise, adds significant scale to our rapidly growing Game Development Service Line, and provides access to a new pool of talent from its base in Portsmouth.
"The studio's excellent track record of high-quality delivery spans over 30 years, with its services in high demand from some of the largest names in the industry.
"We are very excited about the experience and opportunities that Climax will bring to Keywords and our clients, and we look forward to enabling their continued growth as part of the Group."
Climax will become the latest in a line of business decisions made by Keywords. Earlier this month, the company opened a new localisation studio in Paris.