AC Milan have announced the signing of Roma striker Mattia Destro on a six-month loan deal.
Manager Harry Redknapp claimed QPR are unlikely to sign anyone this transfer window despite having cash available.
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."