Discovered by Leicester-based charitable trust Film is Fabulous!, the episodes will be available to stream on BBC iPlayer this Easter.
The episodes from the third series, The Nightmare Begins and Devil's Planet from the show's third series, feature William Hartnell as the Doctor and Peter Purves as companion Steven Taylor.
Hartnell played the first incarnation of the Doctor from 1963 until 1966.
The trust - comprising film collectors and cinema fans - approached the BBC Archives, which restored rediscovered 16mm telerecordings.
BBC archives director Noreen Adams said: "We're thrilled to have worked with the team at Film is Fabulous! to bring these lost Doctor Who episodes to viewers on BBC iPlayer this Easter.
"BBC Archives has been working to restore the original recordings and update these to broadcast quality, ensuring fans can enjoy a little extra treat with their Easter Eggs this April."
The original series aired on television from 1963 to 1989 before being rebooted in 2005.
The most recent season, starring Ncuti Gatwa as the 15th Doctor, aired in 2025.