The 61-year-old, who has been out of work following an 11-game spell with Barnet that ended in January last year, said he was “delighted to help out”.
Former boss Jamie Howell left the club at the weekend with Borough on a seven-game losing streak.
Eastbourne currently sit 15th in the National League South, ahead of Hampton & Richmond and Truro City, although both teams have a game in hand on The Sports.
Speaking to the club’s website, McGhee said: “I live in Brighton, and when the call came to ask if I could assist at Eastbourne Borough I was delighted to offer my services. “I look forward to the challenge of helping to improve what is clearly a progressive club trying to do things the right way.”
In a management career spanning nearly 30 years, McGhee has taken the reins at Reading, Leicester, Wolves, Millwall, Brighton - whom he led to the Championship, Motherwell on two occasions, Aberdeen, Bristol Rovers and Barnet.
He also served as Gordon Strachan’s No.2 in the Scotland national team set-up between 2013 and 2017.
Eastbourne’s next match is against ninth-placed Wealdstone, who sit ten points above them in the table.