For the next generation of Beatles fans, the wait could soon be over.

Apple is expected on Tuesday to announce that it has finally struck a deal with the Beatles, the best-selling music group of all time, and the band’s record company, EMI, to sell the band’s music on iTunes, according to a person with knowledge of the private deal who requested anonymity because the agreement was still confidential.

Depending on the terms of the deal, customers for the first time will be able to buy “Please Please Me,” “Hey Jude” or “A Day in the Life” online rather than on a CD and perhaps even as individual tracks. While the move to digital downloads does not quite rival the band’s first trip across the Atlantic to appear on “The Ed Sullivan Show” in 1964, it is an acknowledgment that online purchases dominate the music industry’s sales strategy.

Apple and EMI declined to comment, and representatives of the Beatles and Apple Corps, the band’s company (not to be confused with the technology company), could not be reached.

One of the last major holdouts against selling its music via digital downloads, the Beatles are the ultimate prize for any music company. The group has held on to blockbuster sales four decades after breaking up — it has sold more than 177 million albums in the United States alone, according to the Recording Industry Association of America — and held on to untouchable cultural prestige.