"The historically low rates we've had are, in part, because of local and international responses to Covid-19 in the past two years.
"As the Reserve Bank moves to rein in inflation and bring some balance back to the economy they have signalled the OCR would continue to rise, potentially to around 3.4 per cent by late 2024. If that happens, interest rates for lending and savings are likely to continue to rise too."
Kelleher said while rising rates would seem daunting for borrowers who hadn't seen it before they were still at relatively low levels and bank affordability assessments did take into account that they may change over the term of a loan.
"The area for people to keep an eye on in the coming months is the impact of rising inflation on their other costs."
He urged any customers who had concerns, or who wanted to take the opportunity to talk about their finances, to contact the bank.
Business borrowers will also see their floating and overdraft interest rates with the bank go up by 0.25 percentage points.
Lorraine Mapu, ANZ managing director for business, said inflationary pressure continued to impact the wider business community including input costs, supply chain issues and a very tight labour market.
"While it has been impressive how our business community has quickly adapted to working with Covid-19, there are some who continue to be impacted by the ongoing disruption caused by the pandemic. We encourage them to talk to us about some of the more targeted measures we can support them with."
The increases will apply to new loans from March 1 and existing loans from March 15.
The bank will also increase its interest rate on its serious saver account by 0.25 percentage points to 0.7 per cent on March 1 and said interest rates on a number of other savings products would rise.