The company was established in 1981 by Leon and Shirley Schollum and it sells a wide range of medical equipment and supplies ranging from dressings through to high definition cameras.
The company is forecasting sales this financial year of about $68m and an underlying profit of $7m.
"The REM management team and employees are looking forward to being part of Paragon Care and the opportunities that will come with this," REM director and shareholder Paul Schollum said.