Completion is subject to regulatory approvals in the United States.
Bank of Ireland and its rival, Allied Irish Banks, dominate the Irish market. Bank of Ireland has been expanding recently in the UK and US.
Great Bay Bankshares has total assets of dollars 319m.
Its loan portfolio of dollars 180m consists mainly of residential mortgages, commercial mortgages and consumer lending.
Great Bay is based in the coastal region of New Hampshire and through its five branches it offers services in south-eastern New Hampshire and southern Maine.
The purchase of Great Bay Bankshares is part of Bank of Ireland's strategy to gain comprehensive coverage of the New Hampshire market and build on its strong franchise there.
Bank of Ireland expects to make significant cost savings when Great Bay is consolidated into its existing US operations, which are dominated by First New Hampshire Bank.
The City also expects Bank of Ireland to make further acquisitions in Britain.
Its name has been linked with Alliance & Leicester Building Society and Bradford & Bingley, although it denies any interest so far.
Its main British operation is Bank of Ireland Home Mortgages, which has pounds 2.75bn on its books.Reuse content