She will head Amplifi’s four divisions – investment, media partnerships, Amnet for programmatic and The Story Lab for branded content – with a team of about 350 staff.
Glucklich was most recently UK chief executive of rival Publicis Groupe’s Starcom until autumn 2017 when she took a break.
"I love agencies," she said, explaining why she was looking forward to returning to the agency world in May when she starts in her new role.
"It’s always been hard to work in agencies. But if you like change and disruption, there’s never been a better time to work in agencies."
Glucklich has experience of both independent agencies such as Arena BLM (now part of Havas Group Media) and network shops such Initiative.
"Dentsu Aegis Network has always been a business I’ve admired for its entrepreneurialism," she said.
Glucklich, who becomes president of Wacl in July, will become a rare female face on the investment side of the media-buying sector, although her role will be much broader than trading.
She will report to Matthew Platts, who previously ran Amplifi and who is promoted to a newly-created role as chief executive of Media Brands UK & Ireland.
"All Dentsu Aegis Network’s media agency leaders across Amplifi, Carat, Vizeum, iProspect, and Fetch will now report into Platts," Dentsu Aegis Network said.
A source dismissed suggestions that the agency brands might be devalued in the new structure and pointed out Dentsu Aegis Network already operates Media Brands as a way to cluster the agencies on a global level.
Stef Calcraft, the UK & Ireland executive chairman of Dentsu Aegis Network, said the grouping of agencies in Media Brands in the UK will help to simplify the offering to clients.
Calcraft said: "In Pippa and Matthew, we have two highly accomplished, inspirational leaders who are greatly respected by both clients, colleagues and the wider media industry.
"Both will play a central role in driving our continued growth and innovation strategy, simplifying our media businesses and delivering superior creative communications solutions for our clients."
Platts appears to be filling part of the role previously held by De Groose who left last October.
Calcraft, a co-founder of independent creative agency Mother, was a surprise choice to head Dentsu Aegis Network because he brought little media experience, although he was a non-executive director of Naked Communications and has an entrepreneurial track record.
Glucklich and Platts both have decades of experience of media-buying.
They want Amplifi to be more client-centric and for Dentsu Aegis Network to operate as a more seamless, connected organisation for advertisers.
Platts said Dentsu Aegis Network already has "a progressive structure that uniquely removes barriers to collaboration and means that we’re set-up to connect our capabilities around our clients".
He went on: "I’m looking forward to working more closely with all our brilliant media leaders to bring our complementary capabilities together, inspire innovation and unlock further value for our clients."
Glucklich’s return to the agency world comes after a string of leadership changes in UK media agencies in the last year.
That culminated in a wave of departures, including Glucklich and de Groose, in October 2017, which was dubbed "Shocktober".
Dentsu Aegis Network manages more than £1 billion in annual billings in the UK.
It has about a 16% of the agency media-buying market in the UK – roughly on a par with Omnicom Media Group and Publicis Media while WPP dominates with more than a third of the market.