Meissner has served as both executive vice president and chief operating officer since joining Goss in 2002 and has previously held management and executive positions with Manroland and Heidelberg.
Chairman of the board Ed Padilla said: "Jochen has been instrumental in the strengthening of our global organisation and our innovative product portfolio over the past six years.
"We are fortunate to have a proven, experienced leader prepared to take our company forward into its next phase."
Brown will continue to be a member of the company's board of directors and is expected to focus on strategic market issues and customer initiatives.
He said: "It has been a privilege to lead such a proud, technology-leading organisation and to work with great employees, printers and publishers around the world."
Goss has nine manufacturing facilities in the US, Europe and Asia, and generated more than $1.1bn (£755m) in sales in 2007.
Goss promotion sees new chief executive appointed
Goss International's board of directors has appointed current chief operating officer Jochen Meissner to succeed Bob Brown as the company's chief executive.
