It is not clear what happened between the chief executive and Mr Morgan.
The settlement is made up of 10 months’ salary – costing taxpayers £146,000 – payment in lieu of notice of £43,800 and accrued annual leave of £19,200.
Officials were said to have argued that the cost of a settlement was cheaper than going through a further investigation and facing a tribunal.
The sources told the BBC that the settlement was voted through by the council’s governing Labour group.
The authority recently took the controversial decision to at least temporarily close Llancaiach Fawr Manor, a Tudor mansion and museum after spending £500,000 a year subsidising the site.
It has also proposed to mothball Blackwood Miners’ Institute.
