Administrator Peter Yeldon has been appointed to the company, a partnership based in Farnborough that is run by partners Derek Jarman, Daren Carter and associate partner Steve Oliver.
A spokeswoman for the administrator said: "The management buyout has been successful and has enabled the continued employment of 85 staff."
Clive Merritt, commercial director at the company, said: "The existing management team has successfully secured the ongoing business of the Midas Press Partnership with an agreed MBO.
"This will enable the continuation of a 40-year tradition with the Midas brand offering top-level, high-quality printing backed by a wealth of experience."
He added that the management team had "received overwhelming support" from its clients and suppliers.
The company was established more than 40 years ago and produces business stationery, point-of-sale items, annual reports and long-run catalogues.
Merritt said: "The Midas Press PLC aims to ensure that its customer's work is professionally managed by a team of highly qualified and vastly experienced print specialists.
"At the same time, continued investment in the latest technology, coupled with 24-hour production, enables the company to successfully meet increasingly demanding timescales."
The company did not comment further at this time.