He will replace Andrew Hodgson, who returns to a full time M&A advisory role after five years as senior partner in Bristol.
Brokenshire has worked with clients and colleagues across the South West, including Bristol, for more than three decades, with a particular focus on advising private enterprise businesses.
Alongside his Plymouth leadership role, he will now lead a 550-strong team of partners and staff in Bristol, advising on tax, audit, deal advisory and consulting matters.
Brokenshire said: “It’s an absolute honour to take on the leadership of the talented team in Bristol.
“As organisations recover from the Covid-19 crisis we have a crucial role to play in driving up the region’s economic recovery across all businesses, from established employers to entrepreneurial start-ups and scale-ups.”
Hodgson added: “It has been a privilege to lead the Bristol office for KPMG. Ian knows the Bristol and wider South West market inside out and he’ll be a fantastic asset for our business.”