The figure is far lower than the value Citigroup had assigned to the Morgan Stanley Smith Barney business on its balance sheet, and as a result Citigroup will take a $2.9 billion non-cash charge against earnings in the third quarter.
Morgan Stanley Smith Barney is the biggest brokerage in the United States with nearly 17,000 financial advisers and $1.71 trillion in assets.
The two banks agreed to the joint venture in 2009 in the wake of the financial crisis. Morgan Stanley, the majority owner, had always expected to buy out Citigroup, but it was unclear how much it would have to pay.
"It was a bad transaction for Citi, but the market has known it was probably going to go against them for awhile, so at least it brings closure," said David Trone, a bank analyst with JMP Securities. "Sometimes you just want to sell something and you'll take whatever price you can get."
On the plus side for Citigroup, its regulatory capital will get a lift from Morgan Stanley buying a bigger stake in the joint venture. The agreement also allows both banks to move forward with plans to realign their businesses.
Both stocks rose on the news. Citigroup shares were up 2.5 percent at $32.64, and Morgan Stanley shares were up 3.3 percent at $17.16 on Tuesday afternoon on the New York Stock Exchange.
The outcome of the dispute was keenly awaited by Wall Street because the decision could shed light on future profitability of the brokerage industry, which has been suffering through low interest rates and weak trading activity for some time.
Under terms of the agreement, Morgan Stanley will buy another 14 percent of Morgan Stanley Smith Barney now and will buy Citigroup's remaining 35 percent stake by June 1, 2015. Each transaction will be based on the $13.5 billion valuation, and client deposits will be transferred to Morgan Stanley at no premium. The deal is subject to regulatory approval.
"As we have shown, the more we put the past behind us, the more we can focus on our future, which is in the core businesses in Citicorp," Citigroup Chief Executive Vikram Pandit said in a statement.
Morgan Stanley CEO James Gorman called the deal a "mutually beneficial agreement" that "gives both parties certainty and transparency on price and timing."
For Citigroup, the sale is another step in Pandit's campaign to shed assets that are not part of the company's plan for the future. Those assets, known as Citi Holdings, at the end of June were down to $191 billion, or 10 percent of total assets, from 36 percent in early 2008.
The two banks brought the matter to an independent arbitrator for an appraisal when they could not agree on a price. But the decision announced on Tuesday was made by the two banks and not the arbitrator, Perella Weinberg Partners, a source familiar with the matter said.
Morgan Stanley's earlier $9 billion appraisal was generally seen as reflecting weak profit while Citigroup's higher price was seen as promising a brighter future.
Citigroup's appraisal worked out to about 50 times current one-year earnings compared with Morgan Stanley's appraisal at 20 times.
Citigroup has been carrying its 49 percent stake at $11.3 billion; the agreement implies it is worth some $4.7 billion less than that. Citigroup had warned of the possibility of an accounting charge to adjust its balance sheet when it disclosed in July how much less Morgan Stanley said the brokerage was worth.
Citigroup will take a charge of $4.7 billion before taxes and a $2.9 billion charge after taxes to reflect the lower value of its remaining stake, the bank said an 8-K filing with the U.S. Securities and Exchange Commission on Tuesday.
Morgan Stanley's 14 percent buy-in will not hurt Citigroup's estimated capital levels under Basel III regulatory measures, Citigroup said.
For Morgan Stanley, buying more of the brokerage is part of a strategy to become less reliant on the volatile securities trading business and the investment banking business, which has been in a long rut.
The joint venture started at a time when the financial markets were on virtual life support from the government, and there were few benchmarks for what the business was worth.
Rather than Morgan Stanley having to raise enough money to buy the assets all once, the companies agreed to share ownership and set a process for Morgan Stanley to buy the rest in increments through 2014. Each side contributed wealth management assets, and Morgan Stanley paid Citigroup another $2.75 billion in cash to take operating control of the joint venture.
Citigroup used the deal to write up the value of its assets to what is essentially its current appraisal, which boosted some measures of its capital at a time when the bank was under pressure because of losses on other assets.
The new valuation announced on Tuesday is expected to have little impact on new capital measurements that regulators plan to use as key benchmarks for bank safety.
Morgan Stanley did not write up its own wealth-management assets at the time of the deal. The two sides were poles apart in valuing the venture ever since, a difference that analysts and bankers say was meant to gain a strategic advantage at the negotiating table.
"Morgan Stanley got a great bargain here in the transactional sense," said Trone. "The problem is, this is a key unit for them, and now they're going to have to spend the next several years convincing the Street that it's worth more than."
As the biggest U.S. brokerage, Morgan Stanley Smith Barney's performance is an indication of how much profit can be had from large-scale wealth-management businesses.
Gorman has made the case that the sheer scale and breadth of the wealth management business, combined with overlaps in lending, investment banking and trading, will give it an edge.
The company is also focused on reducing commission-based accounts in favor of fee-based accounts, which earn money in any market environment.
"The value of wealth management businesses that are composed of a mix of commission income and fee income has gone down since Morgan Stanley purchased the first 51 percent," said Ralph Schlosstein, president and chief executive of the investment bank Evercore Partners Inc .
Morgan Stanley's entire global wealth management business, which includes the joint venture, has been delivering a steady stream of quarterly revenue in a range of $3 billion to $3.4 billion, even in a flat interest rate environment.
That compares with a net revenue range from Morgan Stanley's investment banking business of $851 million to $1.5 billion. Morgan Stanley's trading business has seen revenue range widely from $2.1 billion to $6.4 billion and has lost money in several quarters.
Yet Morgan Stanley's wealth management business has struggled to achieve a long-term profit goal detailed by management at the outset of the joint venture.
Gorman initially said he expected the business to deliver 20 percent pre-tax profit margins over the long term, but last year the company scaled that down to a target in the "mid-teens" by the middle of next year. The business has reached a pre-tax profit margin height of 12 percent on two occasions, including last quarter.
Analysts expect the business to perform better over time as merger costs fall, interest rates rise and market conditions improve.