Fernando Torres is returning to Atletico Madrid on loan until the end of the 2015-16 season.
Steve Clarke is hoping to keep Glenn Murray at Reading after his loan deal expired following the 2-1 win over Norwich.
Carrington, a 29-year-old qualified solicitor, has been on secondment from the Birmingham office of international law firm Squire Sanders since early February, covering the duties of Richard Garlick, who was promoted to the post of sporting and technical director (designate) in January.
He will be responsible for Albion's administrative and legal affairs and will work closely with Garlick, particularly during the summer transfer window.
Carrington told www.wba.co.uk: "I've really enjoyed the time I've spent at the club since February and I'm delighted to have been given this opportunity.
"I've joined the club at an exciting time. I hope to build on Richard's hard work and I'm looking forward to the challenge ahead."