Manager Paul Heckingbottom heralded the signing as a "real statement of intent" as he looks to reshape his squad ahead of next season.
This drew criticism from Mitchell, though, who felt signing a player from the lower leagues of England was "an acceptance of drivel".
He wrote: "Possibly the saddest thing I’ve ever read. Never heard of him; never heard of that team; who is Heckingbottom? All from the team that once brought us George Best. Which WAS a real statement. The acceptance of drivel really gets my goat. We’ve fallen this far? Forest Green Rovers?"
Manchester United legend Best signed for Hibs from Fort Lauderdale Strikers in 1979. The "real statement" played one season at Easter Road but couldn't help the club escape relegation from the top flight following a fifth place finish the year before.
Mitchell was criticised last year after sending out a string of unsympathetic tweets about Leigh Griffiths' mental health issues following news that the former Hibs striker was taking time out of the game to recover.