The Beatles influenced Jimi Hendrix' music, as it influenced an entire generation of musicians. One only need listen to Strawberry Fields Forever back to back with the Hendrix song, Are You Experienced? to realize that Hendrix was after the same audience. 
The first Jimi Hendrix album, Are You Experienced?, peaked on the British charts in 1967 at Number Two. The album that would 
not budge from the Number One slot was the Beatles' Sgt. Pepper's Lonely Heart's Club. 

McCartney warmly relives a memorable event on-camera in the Beatles' Anthology.: "Sgt Pepper was released on the Friday [June 1, 1967] and on the Sunday Jimi Hendrix opened with Sgt Pepper when we saw him at the Savile Theatre. That was the biggest single tribute to me. I was a big fan of Jimi's, and he'd had only since the Friday to learn it." McCartney further described the evening as "simply incredible, perhaps the best I have ever seen him play."

In addition to performing Sgt. Pepper's Lonely Heart's Club many times in concert, Hendrix was also fond of inserting the guitar riff from another Beatles song, I Feel Fine,  into live performances of Hey Joe.

"Paul McCartney, Brian Jones, John Lennon and Mick Jagger in particular became enthusiastic and influential admirers."1

"The Experience... performed before star-studded audiences made up of people like Jeff Beck, Brian Jones, Paul McCartney and John Lennon." 2.

Paul McCartney, as a member of the [celebrity board] for the Monterey Pop Festival, gave the Jimi Hendrix Experience his highest recommendation. The Jimi Hendrix Experience performed the title song from Sgt. Pepper's Lonely Heart's Club
album days after it was released. 

Hendrix' fashion choice of wearing a military jacket may have prompted the Beatles' to wear similar outfits for the Sgt. Pepper album.[more]

1. Electric Gypsy, Glebbeek. p. 113
2. Bold As Love / The Jimi Hendrix Experience, Frank Moriarty. p. 31