The purchase is set to establish Scotland-wide coverage for Chess Group in the storage and interiors market.
ESE will join up with Chess Group subsidiary Modul8 to create new group company - Chess Storage and Interiors.
ESE will be retained within CSI as a separate limited company, both it and Modul8 will continue to trade under their respective identities.
The combined turnover of the businesses is currently £10 million. The value of the deal was not disclosed.
Chess Group chairman James Barrack said: “The companies are leading players in their respective areas of the sector, and make perfect partners to help us optimise our position in the commercial refurbishment market throughout Scotland.”