The 40-year-old has spent the last four years at the north London club, working on scouting, data analytics, financial budgeting and contract management, the academy and athletic development, Villa said in a statement on their website.
Villa's chief executive Tom Fox, another former Arsenal employee, said: "I was able to see first hand the excellent work he did at Arsenal and he will add tremendous value across our entire football set-up."
Villa enjoyed mixed fortunes last season, narrowly avoiding relegation but fighting their way through to the FA Cup final, where they were beaten 4-0 by Arsenal.
They looked destined for the drop in February when they were in the relegation zone having failed to win 10 straight games, before Sherwood was brought in to replace Paul Lambert as manager.
Sherwood, who was widely praised for reinvigorating their season, welcomed Almstadt's appointment.
"I'm really excited Hendrik is joining," he said.
"We have a lot of work to do at the football club and Hendrik will make the job I have here easier."
(Reporting by Toby Davis; editing by Alan Baldwin)
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