Horrell was named the interim chief executive of the business in April and took up the post at the beginning of May.
At the time, Barclays announced plans to restructure its wealth business so it could work more closely with the institution’s retail and corporate banking divisions.
Horrell will report to Barclays chief executive Antony Jenkins.
His predecessor Tom Kalaris retired at the same time as former investment bank boss Rich Ricci, as part of a reshuffle seen as Jenkins’ move to make a clean break with the former regime of ex-CEO Bob Diamond.
Since 2009 Barclays has been building out it wealth-management division as part of a development strategy known as Project Gamma.