The move follows the exit of former competition head Tom Usher, who rejoined SJ Berwin just 18 months after leaving the City firm for Dundas.
It leaves Taylor Wessing with just one competition partner, Martin Baker, in London.
Taylor Wessing senior partner Martin Winter said, “Peter feels his career can be best pursued in another home. We genuinely wish him very well.”
Willis has been a partner at Taylor Wessing for five years. He said he was attracted by the “fantastic opportunity and great challenge” to lead the team, which currently features two associates, at Dundas.
He will be based in London but divide his time between the capital and Dundas’s offices in Scotland. Willis joins Dundas on 7 August.