Up to 55 of 270 jobs are expected to be lost.
Most of these will be through voluntary redundancy, when the Killorglin, Co Kerry-based Fexco officially takes control of the business.
Fexco’s existing stockbroking arm, employing 15 people, is expected to be integrated with Goodbody.
The Central Bank has made no formal comment on granting its approval but AIB spokesman Ronan Sheridan said: “Regulatory approval has been granted and the transaction is expected to be completed shortly.”
The Central Bank said its “regulatory review of the takeover has been concluded and communicated to the firm”.
It declined to give the outcome.
FEXCO has refused to comment on the granting of Central Bank approval.
It is understood that Goodbody’s current managing director, Roy Barrett, 46, and other senior staff will remain with the company in a golden handcuff arrangement.
This will see them get an initial 25% stake in the company, rising to 49% subject to certain performance criteria.
The purchase price is a fraction of the €316m management buyout at rival Davy Stockbrokers when Bank of Ireland sold it off in 2006, and reflects the decline in share trading in recent years.
Goodbody chairman and AIB Capital Markets head of investment banking Mon O’Driscoll will step down and a FEXCO-appointed person, to be approved by the regulator, will be appointed.
Former Tánaiste Dick Spring, who is executive vice-chairman of FEXCO and a board member of AIB, is chairman of FEXCO Stockbroking and expected to become Goodbody chairman.