The Playboy model made headlines when she married a wealthy man in his 80s, then battled his family for his fortune after he died. She later became a reality television personality and died in 2007 of an accidental drug overdose at age 39.
The musical stage work she inspired was created by composer Mark-Anthony Turnage and Richard Thomas, co-author of "Jerry Springer: the Opera," the BBC reported.
"Much of Anna Nicole's life is in the public domain; there's masses of stuff on Google," Elaine Padmore, Covent Garden's director of opera, told the British broadcaster. "But we've had lawyers working with us from the beginning about every aspect of the way it looks and the words we use.
"We don't trash her. People might think we're just taking the mickey out of her at Covent Garden. But we show she had a tough life and came from a very poor background."
The six-performance engagement in London began this week.