Ermotti, a 51-year-old from Switzerland's Italian-speaking Ticino region, was appointed interim CEO in September after Oswald Gruebel quit the Swiss bank over the trading losses.
The board, which had appointed headhunters to find a new CEO, said it had decided to make the appointment permanent after it completed a comprehensive evaluation process.
Weber, who has pushed to join the bank as quickly as possible since the scandal, will be proposed as chairman at the annual general meeting in May, a year earlier than planned.
At the same time, UBS
This strategy will be centered on our leading wealth management businesses and our position as the strongest universal bank in Switzerland, Ermotti said in a statement.
A focused, less complex and less capital-intensive Investment Bank and our asset management business are also key elements for growing our wealth management franchise.
UBS shares were down 1.6 percent at 10.77 francs at 0826 GMT, compared to a 1.0 percent weaker European banking index <.SX7P>.
The appointment represents a rapid ascent for Ermotti, a former UniCredit deputy boss who joined UBS in April. Before UniCredit, he spent most of his early career at Merrill Lynch, where he rose to co-head of global equity markets.
Charming and well-dressed, Ermotti is seen as a bridge builder whose style contrasts with that of the gruff Gruebel who upset Swiss politicians by lobbying against tough capital rules designed to prevent another state bailout of the bank.
Ermotti's most urgent priority is to restore trust with UBS's wealthy private clients following the trading scandal and to scale back the investment bank amid a glut of new regulations for riskier activities.
The definitive appointment of Sergio Ermotti to CEO and also the departure of Kaspar Villiger should be positively received by investors, said analysts Oliver Forrer and Martin Koch at broker Wegelin in a client note.
However the declaration of the CEO today seems to confirm that they are sticking to the disputed business model of an integrated bank they have repeatedly defended, which seems rather disappointing.
Florian Esterer, senior portfolio manager at Swisscanto, which manages some 57 billion Swiss francs and holds over 9 million UBS shares said: I think it's a good step. It was making things difficult having an interim CEO with a chairman who was sort of on his way out as well.
Ermotti's appointment puts him in a much better position to carry out the necessary restructuring at the bank and do the other things he needs to do.
STABILITY AND CLARITY
The nomination of Mr. Weber as chairman of the board and the appointment of Mr Ermotti as group CEO will bring essential stability and clarity to UBS, current chairman Kaspar Villiger said in a statement.
Ermotti has played up his Swiss roots, saying he is motivated by a desire to return his country's flagship bank to its former glory as it prepares to celebrate its 150th anniversary next year.
Near-fanatical about sports as a teen, Ermotti originally wanted to become a ski teacher, but decided against it after an apprenticeship at Corner Bank, a local Ticino lender.
Ermotti's first major task will be to present UBS's new strategy to investors on Thursday when he is widely expected to curb the investment bank, particularly fixed-income activities which soak up large sums of capital.
UBS did not disclose any detail of the strategy, saying only Ermotti and management are authorized to implement it with utmost stringency and diligence.
Investment banking head Carsten Kengeter has so far been spared in the cull following the trading scandal that has claimed Gruebel as well as equities co-heads Francois Gouws and Yassine Bouhara. UBS made no mention of Kengeter in Tuesday's statement.
Swiss financial regulator FINMA and the Swiss National Bank, which manages a fund of mortgage assets offloaded by UBS as part of the Swiss government's bailout of the bank in October 2008, both declined to comment on the appointments.
(Additional reporting by Emma Thomasson; Editing by David Cowell and Mike Nesbit)