The acquisition creates a business with annual revenue of €25m ($27m, £21.3m), employing more than 200 people in more than 60 countries.
Interel said the agencies would "continue to operate under their respective brand names and without any changes in current management for the foreseeable future".
George McGregor, managing partner at Interel UK, told PRWeek there were no client clashes between the two agencies.
He added: "It’s a huge opportunity to migrate business from one business to another. The vast majority of our business is currently in Europe, although we also have offices in India and in China.
"At the moment we have an office in the United States but it’s relatively small, so adding 87 staff will considerably increase our presence in Washington and the US."
Interel CEO Fredrik Lofthagen said: "We already work with a number of the world’s leading associations and societies, as well as many of the world’s best-known corporate brands, but the acquisition of AMG is a further significant step in the successful expansion of Interel as a global player."
AMG CEO J. Bruce Wardle said: "Joining forces with Interel is more than just a geographic or business expansion, it represents a blending of aligned cultures and shared outlooks on the global market.
"It will be exciting to see the affirmative impact this union will have on our clients and professionals, both presently and in the future. I’m also looking forward to continuing in my role as CEO of AMG to ensure the continuity of services and solutions for those we serve."
Interel, founded in Brussels in 1983, was listed 93rd in PRWeek's Global Agency Business Report table of the biggest agencies in the world, with revenue of $14.7m in 2015.
The UK arm of the agency reported revenue of £2.6m in 2015, according to the PRWeek UK Top 150 Consultancies table. The UK arm recently appointed Carl Thomson, previously a director at The Whitehouse Consultancy and former parliamentary assistant to Prime Minister Theresa May when the Conservatives were in opposition, as a director.
A report this week from M&A adviser Results International found that the number of global M&A deals in the PR industry grew slightly last year, as PR firms "fought back" against sister marcoms disciplines by buying agencies to increase their own specialist capabilities.