Mr Boucher, who is currently head of the bank's Irish retail division, will take up the position immediately.
Mr Goggin announced his retirement in January.
Mr Boucher said: 'I am honoured to accept the position of Group Chief Executive.
'In doing so I am very conscious of the current state of the financial services industry, the low opinion in which the general public views banks and the very difficult economic conditions that we face.
'I fully accept that we have an uphill battle as we work towards restoring the trust and confidence of our customers, stockholders and the general public.'
Governor of Bank of Ireland Richard Burrows, said: 'Richie Boucher has a broad range of banking experience and is an outstanding leader.
'I and my fellow directors are confident that Richie will provide strong leadership to Bank of Ireland Group at this very challenging time.'
However, the Opposition has criticised the appointment of Mr Boucher as the bank's new Chief Executive.
Labour's Joan Burton said the choice of an internal candidate to replace Mr Goggin was a missed opportunity to signal a new development in the sector.
She said Mr Boucher was one of a group of bankers who had assured the Oireachtas last year that the fundamentals of the banking system were sound and she asked whether Finance Minister Brian Lenihan had approved the appointment.
Fine Gael's Kieran O'Donnell called on the Government to give details of Mr Boucher's salary and to say whether it was happy with it.
But a spokesman for Bank of Ireland said tonight that the salary of Mr Boucher had not been agreed.
He added that it would be determined by a remuneration committee of the bank's board that would be taking into account the findings of a committee, which as set up by the Government to look at remuneration within the industry.
