Eustace, a former Rams loanee, is a free agent after leaving Watford and he is expected to put pen to paper on the deal this week.
"We have agreed verbally on something for a year, which is great news," Derby boss Nigel Clough told the Derby Telegraph.
"I don't think we have got anybody like John in our squad - somebody to come in and sit in front of the back four.
"I think he will be especially useful away from home. We are looking at trying to remedy the away form of last season when we conceded a few too many goals on the road. He might help in that department.
"He is experienced and a calm head. He is such a good character to have around the place and a good influence on the younger players.
"We are not too blessed with that sort of experience and we are delighted John will be a part of the squad."
Eustace, who spent the final two months of the 2008/09 season on loan at Pride Park from Watford, has featured in three pre-season friendlies for Derby against Bohemians, Port Vale and Bristol Rovers.
The 33-year-old will become the Rams' fifth new signing following goalkeeper Lee Grant, left-back Craig Forsyth and strikers Chris Martin and Johnny Russell.
- Sports & Recreation
- Derby Telegraph