Analysts at Bank Vontobel welcomed the deal, noting that the purchase price for the ING unit was "attractive." Shares in Julius Baer rose 2.4 percent to 40.14 francs ($39.07) on the Zurich exchange.
Julius Baer said it would take on Geneva-based ING Bank Switzerland's 310 employees and expects to recoup the cost of the takeover next year as well as save 35 million francs from combining back-office operations.
The two banks together managed some 160 billion francs for wealthy private clients at the end of August, of which ING accounted for about 15 billion francs.
The deal still requires regulatory approval.