The video shows the guitar-playing Lee miming along to a love song from the album "Asha and Friends" which was released this week.
Lee, who has a rock band called "Six&Out" at home, shot the video during Australia's victorious Champions Trophy campaign in India last month.
Lee, 29, is preparing to spearhead Australia's pace attack against England in the much-awaited Ashes series starting in Brisbane on Thursday.
"Other than cricket, music is my passion. When I was told I would be singing with a legend, I was glad," Lee was quoted as saying in the Times of India newspaper.
The 73-year-old Bhosle was a Grammy nominee in 1997 and in a career spanning six decades has sung for 965 films. She is best known for folk-pop and cabaret.
"Lee sang well, he knows a few Hindi words and is a star," Bhosle told reporters here.
Ashok Mehrotra, who directed the video, said: "Lee is cool headed and was a very focussed artist. We wanted him because he lends charisma and energy.
"It was a great experience, all done in one take."
Lee said he had earlier turned down an offer from another Bollywood legend Amitabh Bachchan, made when he visited Mumbai on his way home from Australia's tour of Bangladesh in April, to play the lead role in a movie.
"I said 'mate, I've had no acting experience in my life' and he told me that was OK, they could sort that out," Lee was quoted as saying.