Hall, formerly the chief executive of Saatchis' New Zealand operation, has held the top role in London for two-and-a-half years.
He is expected to join a new venture being set up by his former colleagues Kim Thorp, who has been with Saatchis' for 16 years, including 12 as the creative director at the Wellington office, and Peter Cullinane, who was worldwide chief operating officer until his resignation in January.
Dundas joined Saatchis' four years ago as the executive planning director from FCB San Francisco, where he held the dual roles of executive vice-president and director of planning. He will run the agency in partnership with the executive creative director, Tony Granger.
"We have come a long way in the past couple of years and my brief is to take the agency to the next stage," Dundas said. "It is a good time to look at how the agency is run. All the management teams are in place but I will review the structure as we go forward. A key element is the managing director role and I will be looking at all the options."
Hall will continue to work in the London office until the end of the year to ensure a smooth transition of power.
"This has been planned for a long time as it has always been known that James wasn't staying forever, Kevin has been prepared for this for a while," Granger said. "James will be like a Godfather until he heads home. Kevin will make decisions and I will be by his side."
The decision to promote Dundas was made jointly by Saatchis' worldwide chief executive, Kevin Roberts, and the European chairman, Richard Hytner, who has just taken up his new post after being appointed in July.
"We respect James' desire to return to New Zealand with his family which he has been considering for some time," Hytner said.
"We are very grateful for his terrific contribution to the company. I have long admired Kevin, he is passionate about ideas and a great standard setter. He and Tony will make a great team."