The Treasury Department said Monday afternoon it planned to sell 2.4 billion Citi (C) shares in an underwritten offering. Treasury said later in the evening that the offering was priced at $4.35 a share — giving the government a $12 billion profit on its $45 billion Citi bailout.

The government paid the equivalent of $3.25 a share for its stake in the No. 3 U.S. bank by assets. Counting stock sale proceeds, dividend payments and interest on bailout loans, the government got $57 billion in compensation for the Citi bailout, Treasury said.

“Selling off the remaining stake ensures that taxpayers will book a healthy profit on their Citigroup investment,” said Linus Wilson, an assistant finance professor at the University of Louisiana at Lafayette and a longtime bailout tracker.

The announcement comes at a good time for the government, with policymakers taking their latest bailout beating courtesy of newly released details of the Federal Reserve’s crisis lending. Though the bank bailouts have proved far less costly than early estimates suggested, they remain deeply unpopular due to a failure to hold major crisis players — from bankers to government — accountable for their misssteps.

It also comes just under a year after Citi and the government reached an agreement that cleared the way for Citigroup to repay the massive bailout package the government provided during the darkest days of late 2008 and early 2009. That deal also gave the feds a deadline next week to complete their share sales.

The government gave Citi $45 billion in Troubled Asset Relief Program loans during the crisis. Last December’s deal, together with one reached earlier in 2009 to convert much of the government’s TARP preferred stock to common shares, left the feds with a staggering 7.7 billion shares of Citi, representing a 27% stake.

This past spring, Treasury started dribbling the shares into the market. The government managed to reduce its stake by about two-thirds without affecting the stock price, Wilson’s research showed.

The slower-than-expected pace of those sales leave the feds holding a sizable chunk of Citi shares as the one-year anniversary of last year’s deal looms. But Citi shares have actually risen over the past month, in spite of declines in the bank stock index amid concerns about Europe’s solvency and the banking industry’s legal exposure to what is being called foreclosuregate.

Wilson said the government averaged nearly $4 a share on Citi stock sales through October, and since then the feds have managed to sell an added 900 million shares at a time when the market price has generally been rising.

The government will still hold warrants for Citigroup’s common stock that were issued as part of Citigroup’s participation in Treasury programs, Treasury said, and the government could get up to $800 million in trust preferred securities unless the Federal Deposit Insurance Corp. loses money backing Citigroup debt under the Temporary Liquidity Guarantee Program.

But broadly speaking, Citi and the feds will be free of one another for the first time since the crisis, which is an arrangement everyone can be happy with.

“I am glad that the U.S. Treasury has taken steps today to keep its promises to Citigroup’s investors and managers sell taxpayers’ stake by December 14, 2010,” Wilson said.