It is the first significant move by the agency's newly appointed chief executive, Farah Ramzan Golant. Brazier becomes only the third executive creative director at AMV, the UK's biggest advertising agency.
Brazier has been charged with returning the agency to its former creative glory. Ramzan Golant said: "Paul embodies the relentless search for great ideas that is at the core of AMV."
Paul Belford and Nigel Roberts retain their roles as AMV's creative directors, while Souter will maintain his client-facing role with Royal Mail and PepsiCo.
Following a four-year stint at WCRS, where he teamed up with Souter, Brazier joined AMV in 1991. He partnered Nick Worthington in 1997, when Souter became the executive creative director.
Brazier has worked on a long list of highly regarded ad campaigns, including The Economist "shredder" and Wrangler "rodeo".
More recently, he created the Guinness "mustang" spot, which was directed by Anthony Minghella.
Brazier said: "Good ideas are the most important thing. When someone does something good, it lifts the whole agency. As a creative, I just try to handle things as they come along and this is how I'll be treating the new role. It's definitely a big job, but I have been here a long time and I know how the agency works."
Ramzan Golant explained: "Paul has been friends with Peter for years and they have always worked closely together. They came to AMV as young bucks and have been studded around the company.
"But Paul is more than capable of taking over Peter's role and will want to run things in his own way."
AMV was founded 27 years ago, with David Abbott as its founding creative director.
If you have an opinion on this or any other issue raised on Brand Republic, join the debate in the .