The investment in the £2.7m-turnover company, which is based in Milton Keynes, will "enhance capabilities in the UK", according to Bong chief executive Anders Davidsson.
"The acquisition is in line with Bong's strategy to broaden our share of the direct mail market," he added.
Image Envelopes was founded in December 2006 and has grown rapidly to its current £2.7m turnover.
Managing director Mark Jeffery said: "This offers us enormous possibilities to enhance our customer offering. We can maintain our flexibility and speed of service, while enjoying the benefits of the larger group leverage and a wider range of products."
Bong has annual sales of over SEK2bn (£200m) and employs 1,200 employees across 12 countries. It is listed in Stockholm on the Nasdaq OMX index.