KKR and a group of investors agreed to purchase a 5% minority stake in TeamSystem.
Francisco Partners will acquire a separate 10% stake in the Italian software provider.
The transaction values the accounting and business management software firm between €8 billion and €10 billion.
Primary investor Hellman & Friedman is selling the stakes to partially cash in while retaining a holding.
The deal occurs as artificial intelligence concerns create valuation pressures across the software sector.