Universal was the only bidder remaining for EMI's recorded music division, the home of Katy Perry, Coldplay, The Beatles and Pink Floyd, after previous favourite Warner Music pulled out of the running.
Reports have suggested that the other half of EMI's business - the lucrative music publishing division - will be sold to a Sony-led consortium for in excess of $2bn.
Citigroup took control of the 114-year-old EMI Group in February after previous owner, Guy Hands's Terra Firma private equity vehicle, could no longer support the label's debts and failed a solvency test.
EMI's labels include Blue Note, Capitol, Parlophone and Virgin Records.
Universal Music, which is a unit of French media giant Vivendi, oversees various labels including Def Jam, Motown, Decca, Island Records and Interscope Records.
EMI Group chairman Stephen Volk, who is also vice chairman of Citigroup, said: "We believe that this transaction accomplishes Citi's objective of maximising the value of EMI, giving EMI Music a partner in Universal Music that appreciates EMI's rich cultural legacy, its incredible stable of musical talent, and its employees who work so hard to deliver successful outcomes for the artists they represent."
Universal Music chairman and chief executive Lucian Grainge described the deal as a "historic acquisition" for Universal and "an important step in preserving the legacy of EMI Music".
He added: "For me, as an Englishman, EMI was the preeminent music company that I grew up with. Its artists and their music provided the soundtrack to my teenage years. Therefore, UMG is committed to both preserving EMI's cultural heritage and artistic diversity and also investing in its artists and people to grow the company's assets for the future.
"As a result, we will be better positioned to fully capitalize on the many new and exciting opportunities in the current marketplace, and also able to better serve our artists, songwriters and business partners, while offering fans even more choice."
Terra Firma acquired EMI in 2007 for £4.2bn, but then the credit crunch hit and the private equity vehicle struggled to meet payments on the £2.6bn it had borrowed from Citigroup to fund the deal.
After losing control of the record label, Terra Firm attempted to take Citigroup to court in the US over the price it had paid for EMI, but ultimately the firm lost the case.
Vivendi said that the deal for EMI Music has been approved by its board, but it is still subject to "approvals of regulatory authorities in the countries and continents concerned".