The departures are the latest step in the board's remaking itself after Citigroup's disastrous performance during the financial crisis prompted three separate government rescues. Citi has repaid the money it owes the United States, but the government still holds 7.7 billion of the bank's shares.
Zedillo's nomination is a signal of the increasing importance of Banamex, Citigroup's Mexican banking unit, to the broader company, analysts said.
Some regulators pushed the bank to sell the Mexican unit last year, but Citigroup refused and said Banamex was a key part of its strategy. Since then, Banamex head Manuel Medina-Mora has become Citigroup's head of consumer banking for the Americas.
Armstrong, a former chief executive of AT&T
Armstrong was swept up in a scandal involving Sanford Weill, a former chief executive of the bank, and then-Citigroup telecom analyst Jack Grubman.
Mulcahy, Xerox Corp's
Citigroup's board has long been criticized for being excessively deferential to the bank's chief executive, and for lacking the expertise to identify problems at the company, particularly during the financial crisis.
Regulators pressed Citigroup last year to add directors with more financial expertise. Until 2009, many of Citigroup's board members dated back to Weill's era, or earlier.
Weill, who cobbled together Citigroup from various other financial services companies, was replaced by Chuck Prince, who in turn stepped down in 2007 soon after announcing huge expected credit losses, in what would prove to the first of many brutal quarterly announcements from the bank.
The jury is still out on how well Prince's successor, current CEO Vikram Pandit, will do at restoring the third largest U.S. bank's fortunes.
Citigroup's shares rose 1 cent to close at $3.40 on Friday. The bank's shares are likely to remain in a tight range until investors have more clarity about when the government will sell off its 7.7 billion of Citigroup shares, analysts have said.
But even before the financial crisis, experts criticized the bank's board. In 2003, research group the Corporate Library rated Citigroup's board the least effective of the 1,700 companies it evaluated.
The Corporate Library cited a scandal that emerged in 2002. Grubman wrote an email to a friend in which he bragged that he wrote a positive report about AT&T in order to curry favor with Armstrong, who in turn would vote according to Weill's preference.
Weill could then help Grubman's children get into an exclusive pre-school, according to the analyst's email. Weill and Grubman later said that there was no connection between AT&T's upgrade and Armstrong's vote.
The Corporate Library called this one of the most outrageous scandals of the most scandalous year for American business since the 1929 stock market crash. The research group criticized Citigroup's board for failing to hold Weill accountable and for awarding him large compensation packages.
In 2009, under pressure from regulators, Citigroup's board added directors with financial expertise, including Anthony Santomero, former president of the Federal Reserve Bank of Philadelphia; former U.S. Bancorp
Armstrong and Mulcahy said they would not seek re-election at the shareholder meeting, according to a statement from the board.
Another board member, John Deutch, said earlier this year he would not seek re-election. In an interview with the Wall Street Journal, he urged other directors who sat on the bank's board during the financial crisis to step down in an orderly fashion.
Zedillo, 58, an economist by training, was president of Mexico from 1994 to 2000.
(Reporting by Dan Wilchins and Steve Eder; editing by Gerald E. McCormick, Steve Orlofsky and Leslie Gevirtz)