PAI bought the business in 2013 in a deal that valued it at €465m.
Advent intends to combine the business with Brammer Group, a UK manufacturer that the firm took private earlier this year.
IPH provides industrial products and services to clients in the chemical, pharmaceutical, food processing, energy, transport, automotive, petrochemical and mechanical engineering sectors across Europe. It reported revenues of €1.3bn for 2016.
The combined group will have annual revenues of around €2.1bn.