Stephens and Nielsen will become joint creative directors and will run one of the UK agency's four groups. They will work across between eight and ten accounts. Their portfolio of clients is expected to include Nescafe and Greene King.
They are the second senior team to leave Leo Burnett in two months. In October, Steve Jones and Martin Loraine, who created John West's "shark" spot and the McDonald's "divorced parents" ad, moved to BMP DDB.
Stephens and Nielsen, who will start at the end of January, are likely to have around five teams reporting to them. They will be two of eight creative directors in the department and will report in to the executive creative director, Luke White.
Stephens, 35, and Nielsen, 41, have worked together for seven years.
During their five years at Leo Burnett, they worked on Nintendo, Holiday Inn, McDonald's and the Heinz brands Salad Cream, Baked Beans and Babyfood.
The team's Salad Cream campaign won a Creative Circle gold, a Cannes silver award and an IPA Effectiveness award.
They first teamed up at D'Arcy in 1995, where they worked on Littlewoods Pools and COI Communications' child road safety campaign. Before that Nielsen worked at Mustoe Merriman Herring Levy, WCRS and J. Walter Thompson.
Stephens worked at Bainsfair Sharkey Trott and KHBB.
White said: "From what I know of them, they're very good at strategy. They're also very professional and fired up about contributing to what we're doing here. They had a glass ceiling at Leo Burnett, but I've offered them a wider-ranging role here."
Stephens added: "We feel like we're ready for a new challenge. We want to run a group and run accounts, and McCann will give us that opportunity."
White has also boosted the agency department with the imminent arrival of Sarah Barclay as a creative director to run Coca-Cola. Barclay joins in January from BBDO New York.