Net profit at the bank, which specialises in wealth management, fell to 258.1 million francs ($279 million) and profit before taxes dropped 26.6 percent to 318.8 million, it said in a statement.
Bär cited the impact of the strong franc and an exceptional charge of 50 million francs related to the bank's move to axe 150 posts, announced in November last year.
The bank also had to pay a one-off sum of 50 million euros to German authorities to close a tax evasion probe.
Net inflows for 2011 grew 15.9 percent to 10.2 billion francs, mainly from Asia, Russia, Eastern Europe and Latin America.
The group's local business in Switzerland and Germany also delivered "significant" inflows, the bank said.
"We were able to maintain our groups business momentum in most dimensions in 2011 despite a challenging market and business environment," said chief executive Boris Collardi in a statement.
Bär said it would "continue to cooperate fully" with authorities in the United States who are investigating banks suspected of helping American clients avoid paying tax.
"Julius Bär is strongly committed to resolving this situation and is confident that a mutually satisfactory solution will be found," the group said.
The bank will offer its shareholders a total dividend of one franc per share and launch a new share buyback programme with a maximum value of 500 million francs to be carried out over two years.
Its share price was down 4.4 percent to 36.16 francs towards 1030 GMT.