Candy Crush Saga, Dirt Rally 2.0 and Sniper Elite 4 are among the games that will feature the messaging.
The initial ads will focus on the theme: "Stay home. Save lives."
Rebellion - one of the companies involved - also publishes 2000AD among other comics, and has also offered space in these for the government's campaign.
"I reached out to DCMS [Department for Digital, Culture, Media and Sport] a few days ago to say is there anything we can do," Jason Kingsley, chief executive of Rebellion and chair of the games trade body Tiga told the BBC.
"A lot of people spend hundreds of hours in computer games.
"And in this case, we thought we could help society by reminding people of their obligations to others."
The inclusion of Codemasters' off-road racing game Dirt Rally 2.0 comes a day before it is included in Sony's latest PlayStation Plus package. This should give it a high profile over coming weeks, and ensure many thousands of subscribers see the in-game ads despite the title being more than a year old.
Likewise, Activision Blizzard's London-based division, King, predicts millions of gamers will see the ads within its mobile games, which include Farm Heroes Saga in addition to Candy Crush.
The games creators will feature the promotions in different ways.
In Rebellion's case, it will display the message on a screen shown before gameplay begins within its Strange Brigade and Sniper Elite titles. It normally uses the launcher pages to promote its other wares. In the case of PC gamers, the pages will also contain a link to a website containing further advice about the virus.
By contrast, Codemasters will take advantage of the fact it has built in the ability to display ads within the action itself, which it can remotely update. The tech for this is supplied by the London-based start-up Bidstack.
"We realised that technology within our games, which enables the remote updating of banners within the virtual environment, could be repurposed to assist with the coronavirus communication effort," Codemasters' business development chief Toby Evan-Jones explained.