The bank, which will today open its first branches in Dublin and Limerick, said regular savers can open a monthly deposit account offering 3.75% - 0.5% higher than the best rate currently available.
The account is the first of six new products due to be launched by the bank.
The savings market is highly competitive, with the main banks already fighting for customers with the likes of foreign operators Northern Rock and RaboDirect.
The account, which requires a minimum monthly deposit of €10, pays 0.5% more than the comparable AIB account and is 2% higher than a similar Bank of Ireland offering.
Bank of Scotland's competitive pricing is expected to be a feature of its products. It plans to offer credit cards, home, car and personal loans and insurance. However, it will not be able to offer personal current accounts for another year.
"There are big existing banks... who are rather comfortable with the status quo and haven't hitherto faced the scale of opposition that we propose," said James Crosby, group chief executive of Bank of Scotland's parent company HBOS, yesterday.
Bank of Scotland has spent €160 million getting into the retail market. It bought 54 shops from the ESB last March and has been converting these into branches since then.
The bank said it will open 46 branches this year and may consider more if there is demand from consumers.
The branches will be open for longer than rivals on weekdays and will also open on Saturday mornings, a move the bank says has been popular.
While Bank of Scotland said there has been an "inertia" among consumers to switch banks, it believes that cost savings will be attractive to consumers.
And the bank is not entering the market without an existing customer base. It has a 6% share of the mortgage market and a 15% of the car finance market.