Councillors voted 29-23 in favour of the deal at a meeting in Haverfordwest on Thursday.
Mr Parry-Jones will leave his post on 31 October.
This deal follows a row over cash payments in lieu of pension contributions which the Wales Audit Office said were unlawful.
Police inquiries into the cash payments have been dropped after no evidence was found of criminal offences.
Dyfed-Powys Police said no further action would be taken following two investigations by officers called in from the Gloucestershire force.
Paul Miller, who leads the opposition Labour group on Pembrokeshire council, said: "I am bitterly disappointed at the level of the settlement which is completely out of kilter with the lives of the people we represent.
"There was a disciplinary process under way and that process should have been allowed to reach a conclusion. In my view, if it had been allowed, the people of Pembrokeshire would not be so much poorer this afternoon."
Mr Parry-Jones is the highest paid council chief executive in Wales with a salary of almost £195,000 plus benefits in kind.
But following the Wales Audit Office report in January into the cash payments, he has been under pressure to resign from the post he has held for nearly 20 years.
In July, Pembrokeshire council said it would take no further action to reclaim the money from him or another unnamed senior officer involved in a similar arrangement.
The chief executive took a "leave of absence" in August, but it has since emerged it coincided in part with his annual leave.
The proposal for a severance deal for Mr Parry-Jones was confirmed to BBC Wales earlier in October by a member of the council's disciplinary investigation committee.
Mr Miller said earlier that any discussion over such a package "should be held in public gaze".
However, councillors voted to discuss the severance package in private.
A severance deal worth £330,000 has been agreed for Pembrokeshire chief executive Bryn Parry-Jones to quit his job, BBC Wales understands.