The deal, confirmed today, will see the BASF and ANI (formerly Akzo Nobel Inks) merged to create a new business with sales of more than Euro830m (572m).
A potential sell-off of the BASF business has been the subject of speculation for several weeks.
BASF Printing Systems employs 2,600 staff worldwide, while ANI employs 960.
In a joint statement the companies said the sale "should enable the printing systems business to emerge as a leading international supplier in the industry". The terms were not disclosed.
CVC managing director Dr Christian Wildmoser said: "We are making a decisive contribution to consolidation in a fragmented industry. As a result of the acquisition BASF Printing Systems will become a core business."
He said the merged entity, which will be headquartered in Stuttgart, would "not only be able to maintain its market position, but expand it further".
Charles Murray, corporate vice president and group managing director at Sun Chemical, the world's largest ink maker, commented: "It's good news in that it brings more consolidation to the industry, but it's going to do nothing to reduce overcapacity it simply reduces the number of players.
"It needs to be recognised that the current state of the printing ink industry meant that no-one else was prepared to buy it. A concerning number of ink makers are now owned by financial institutions, rather than companies that are dedicated to the industry," he added.
Story by Jo Francis