The 52-year-old takes over at the Spireites after leaving Barnet last week, writes Tom Feaheny.
He's been manager of the North London club on five different occasions, and gained promotion with them to League Two in 2015.
Allen was at Vanarama National League side Eastleigh as well previously.
Speaking about his appointment at a press conference he said.
"There are players who can come in now, we are in a position to recruit as soon as we want."
Allen will be joined by the ex Chesterfield goalkeeper Carl Muggleton who joins as part of his coaching staff.