Jonathan Lewis, the founder and managing director of Outdoor Plus, said Inflexion "shares our vision for growth" and he plans to "use their investment to continue to deliver the best sites in the best locations".
Nigel Sharrocks, a former senior executive at Dentsu Aegis Network, has been appointed as non-executive chairman of Outdoor Plus after Inflexion introduced him.
Lewis has invested heavily in digital in London and sold off most of his company's traditional billboards in recent years and close to 90% of revenues come from electronic screens such as The One Knightsbridge on the Hyde Park underpass.
Outdoor Plus is thought to be worth more than £50m, based on an estimate of double this year's revenues. Lewis declined to reveal the value of the sale.
Turnover in its last financial year is estimated to be £25m, based on its most recent accounts that covered a nine-month period.
The shareholder register of Outdoor Plus boasts a number of big names from UK media and a veteran rock star.
Phil Georgiadis, chairman of Blue 449, former Havas bosses Marc Mendoza and Mark Craze, and Nick Mason from rock band Pink Floyd all hold small stakes.
It is thought some investors will hold onto their stakes while others plan to sell some or all of their holding.
Simon Turner, managing partner at Inflexion, said: "We are delighted to be recommended to Jonathan and his team as the minority investor of choice, enabling him to find the right investment solution to suit his growth ambitions for Outdoor Plus.
"Inflexion brings strong TMT sector experience to support the business expansion plans [of Outdoor Plus]."
Lewis said Inflexion's investment made sense partly because the private equity firm has a "knowledge and understanding of the sector".
Inflexion said it tends to make investments of between £10m and £100m in "high-growth" businesses. Its other investments include media production house Group IMD.
Outdoor Plus is about number six in the UK out of home market behind JCDecaux, Clear Channel, Exterion Media, Ocean Outdoor and Primesight.
All except JCDecaux now have private equity investors, making consolidation in the sector more likely.
Lewis founded Outdoor Plus in 2006. The company claims the UK digital outdoor ad market has been growing at over 25% a year since 2010.