Her first assignment will be the Euro/Africa Zone Group 1 ties in Tallinn, Estonia following next year's Australian Open.
London-born Keothavong, whose brother James is a top-level umpire, retired, aged 29, in 2013 and has been working as a TV pundit for BT Sport since.
She reached a career-high ranking of 48th in 2009 - the first British woman to crack the top 50 for 16 years.
"I think Anne is a great choice as our next Fed Cup captain," British number one Johanna Konta said.
"She will lead from real life experience because she was a winner on court and she knew what it took to step up and play for her country."
(Reporting by Martyn Herman, editing by Ed Osmond)
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