Chief financial officer Michelle Jablko said ANZ's return on equity and earnings per share will be subject to a "small impact".
ANZ did not give a price tag for the transaction but said the impact on its bottom line - including writedowns and transaction costs - will be a net loss of about A$265 million.
It will be initially higher in the first half of the bank's 2017 financial year but will be offset back as the sales progress over future periods.
A trading halt placed on ANZ's shares ahead of the announcement on Monday was lifted an hour after the market opened.
At 2.20pm, the shares were up 28 cents, or 1.01 per cent, at A$27.90 - broadly in line with gains by rivals Commonwealth Bank and Westpac.
DBS will acquire 1.26 million customers across the five countries, and deposits of about A$17m. About 80 per cent of staff will move across.
The businesses being sold are expected to contribute A$825m of revenue and A$50m in cash profit to ANZ's 2016 full-year results, due on Thursday.
In May, the bank cut its interim dividend for the first time in seven years after first-half cash profit dropped 24.3 per cent, with a A$260m impairment on its investment in Malaysia's AmBank among the one-off hits.
ANZ said its focus in Asia will now be institutional banking across 15 countries.
"In retail and wealth, although we have grown a profitable business in Asia, without greater scale ANZ's competitive position is not as compelling," Mr Elliott said in a statement.
"To make a real difference for our retail and wealth customers, we would need to make further investments in our Asian branch network and digital capability ... (which) do not make sense for us given our competitive position and the returns available to ANZ."
The sales are subject to regulatory approval and are expected to take 18 months.