Wyndeham's board have unanimously approved the 1.55 per share offer, which values the firm at 80.6m.
"We looked at it [the approach] from a shareholder perspective," said Wyndeham chief executive Paul Utting (pictured). "The bid made does represent good value for our shareholders and it's good for the ongoing development of the business."
The Icelandic firm's chairwoman Thordis Siguroardottir said the deal would give it a foothold in the UK.
"We announced six months ago that we were going to double in turnover and we're looking for acquisitions abroad, in Scandinavia and the UK," she said. "We looked around and we found Wyndeham.
"It's a great company with fine profitability, excellent relationships and in a leading market position it's a good investment."
"Dagsbrn fully supports the existing strategy of Wyndeham," said Utting. "And the weight Dagsbrn has in terms of its other activities will add to the business."
On Dagsbrn's planned expansion here and elsewhere, he added: "Hopefully, we'll be the spearhead of that."
The existing UK management team are all staying.
Wyndeham has been acquisitive itself recently, snapping up repro firms Icon Reproduction and Connect Digital Imaging, and digital and large-format printing outfit Blacketts in the past year.
The offer is open for acceptance until 14 of April and is conditional on the purchase of 90% of shares.
Yesterday (23 March) the firm issued a statement that it had received an offer following a dramatic rise in its share price. Dagsbrn was not one of the firms tipped as a possible buyer, and its move was described as "totally left field" by a number of sources.
The firm is the owner of Iceland's largest broadcasting and print firms, 365 Broadcasting and 365 Print Media, and Iceland's oldest print works.
Its largest shareholder, with 24.9%, is Baugur Group, which owns several UK firms including supermarket Iceland, food wholesaler Booker, jeweller Mappin & Webb, toy store Hamleys and fashion retailers Jane Norman, Oasis, Karen Millen, Coast and Whistles.
