The 34-year-old midfielder signed on a free transfer, penning a one-year deal, earlier this week after impressing on trial.
He will provide competition for places in central midfield following the departure of Saidou Khan and while Manny Oyeleke is on the sidelines.
Jones was a free agent after being released by League Two Barrow.
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He has two promotions on his CV with Bury and Sheffield Wednesday and has played around 500 appearances in the EFL.
The Birkenhead-born man has also played for Tranmere Rovers, Oldham Athletic and Carlisle United.
On Jones, Cook said: “He is a great lad, he is very physically fit.
“He lives his life really properly off the pitch to be a footballer.
“His habits around the training ground and the dressing room are everything that I like.
“He does his gym work and he has a relationship with the younger players.”
Jones, who became Chesterfield’s 12th summer signing, has been at the Spireites since the very start of pre-season.
Cook added: “He is what I like to call a really good role model.
“And he can also play football as well which doesn’t half help!”