A2 chairman David Hearn said the company was going through a period of continued strong growth in dynamic markets and Bortolussi's "skillset and comprehensive strategic and operational experience will serve the company well".
Bortolussi will start with a2 Milk early next year.
His appointment follows the surprise departure of Jayne Hrdlicka late last year after less than 18 months in the top job.
Former chief executive Babidge returned to the job in January - on a salary of A$1.6m - while the company made a global search for a new CEO.
Babidge, who is credited with turning the once almost-insolvent alternative milk company into today's multi-billion-dollar operation, ran the company from 2010 to 2018.
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A2 Milk commercialises intellectual property relating to A1 protein-free milk, which is sold under the a2 and a2 Milk brands, as well as the milk and related products like infant formula.
The company says its a1 beta-free protein can benefit those who have trouble digesting standard milk.
In stepping down, Hrdlicka, a former executive of cut-price airline Jetstar, said the a2 Milk job would have involved more much travel than she had anticipated.
Despite reporting a hefty lift in its annual net profit for 2018-19, a2 Milk's share price took a big hit last August when it transpired that the company would spend more on future growth.
In a trading update issued in April, a2 Milk said it continued to experience strong revenue growth across all key regions, particularly of infant nutrition products sold in China and Australia.
It said then that it expects revenue for the full year to lift by 30 per cent to around $1.7 billion thanks to strong sales growth as consumers rushed to fill their pantries with infant formula as a result of the Covid-19 pandemic over the March quarter.
In its April update, the company said it had continued to experience strong revenue growth across all regions since the release of its six-month result in late February.
It lifted its earnings margin forecast 31 to 32 per cent for the year to June from an earlier advised 30 per cent.
The company was benefiting from the unusual combination of pantry stocking, a very weak exchange rate, and lower costs - all consequences of Covid-19.
The upgrade implied full year ebitda $527-560m, compared with market consensus forecasts of $520m, and compared with the the previous year's ebitda of $413.6m.
A2 Milk, with a market capitalisation of $15 billion, is New Zealand's second biggest stock.
The company's annual result is due on August 19.