The 21-year-old attacking midfielder has apparently penned a two-year deal with the Spireites, reports East Anglian Daily Times.
The Tractor Boys confirmed his exit from the club by ‘mutual consent’ earlier today.
The Albania under-21 international has made 30 appearances for Ipswich after coming through the academy.
Dobra made three appearances under Cook when he was in charge at Portman Road.
He becomes the second Ipswich player to move to Chesterfield this summer following Bailey Clements’ move.
Dobra, who was loaned out to Colchester United last season, will become the Spireites’ ninth summer signing.
“Everyone at Ipswich Town wishes Armando all the best for the future,” Ipswich said in a statement.