The firm was dubbed "Team Jorge" by investigating journalists who posed as potential clients in order to gather information on its methods and capabilities.
Its boss, Tal Hanan, is a former Israeli special forces operative who boasted of being able to control supposedly secure Telegram accounts and thousands of fake social media profiles, as well as planting news stories, the reports say.
Most of the campaigns -- two-thirds -- were in Africa, he claimed.
"We are now involved in one election in Africa... We have a team in Greece and a team in [the] Emirates... [We have completed] 33 presidential-level campaigns, 27 of which were successful," the Guardian quoted him as saying.
While demonstrating his technology to reporters, he appeared to hack into the Gmail inbox and Telegram account of political operatives in Kenya days before a presidential election there.
Forbidden Stories named the targets as two aides to William Ruto, who ended up winning the August 2022 ballot.
Online public influence campaigns were carried out via a software platform, known as Advanced Impact Media Solutions, that allegedly controlled nearly 40,000 social media profiles across Facebook, Twitter or LinkedIn, the reports say.
The investigation into the Israeli firm's operations was carried out by a consortium of journalists from 30 outlets, including the Guardian in Britain, Le Monde in France, Der Spiegel in Germany and El Pais in Spain, under the direction of the France-based non-profit Forbidden Stories.
"The methods and techniques described by Team Jorge raise new challenges for big tech platforms," the Guardian wrote.
"Evidence of a global private market in disinformation aimed at elections will also ring alarm bells for democracies around the world."
Hanan did not respond to detailed questions, saying only: "I deny any wrongdoing."
