Written by Jeff Lynne in 1971, it was one of two songs featured on the B-side of the UK hit "California Man" credited to The Move (the other was Roy Wood's "Ella James"). In the US the B-side proved to be more popular than the A and so the song became The Move's only hit in the US albeit a minor one (number 93 on the Hot 100 chart). The song was originally titled "Look Out Baby, There's a Plane A Comin'" (which is sung by Wood at the end of the song). The song was later included on the 2005 remastered version of the Message from the Country album, in both the original single version and an alternate take.
The song was recorded on the same multireel tapes alongside the Electric Light Orchestra (ELO) tracks "From the Sun to the World" and "In Old England Town", the two songs that Wood appeared on from the ELO 2 album.
Electric Light Orchestra (ELO) began to perform "Do Ya" live with Lynne on lead vocals during 1973–75, and they recorded it in the studio for inclusion on their 1976 album A New World Record. In a 1978 interview for Australian radio stations 2SM and 3XY, Bev Bevan stated the reason for the re-recording was that after ELO had added the song to their live performances a music journalist asked the band their opinion of "the original version" by Todd Rundgren. (Utopia, a band Rundgren started in 1974, had been performing "Do Ya" in concert.) Bevan said they decided to re-record it as ELO in order to "let everyone know that it's a Jeff Lynne song."
In 2000, Lynne found an unedited alternative mix for the song, also recorded in 1976, that he decided he preferred over the album cut. A digital remaster of the track is included on the compilation box set Flashback.
The song inspired Tom Petty to write the US hit single "Change of Heart" in 1982. In 2002, Tallboy Records released a tribute disc of "Do Ya" in the form of a 7" extended-play single, featuring renditions of the song by Kenny Howes and the Yeah!, Parallax Project, Einstein's Sister, and Linus of Hollywood.