The credit at the end of the programme said: "Ncuti Gatwa as the Doctor. Jodie Whittaker as the Doctor. And introducing Billie Piper".
In a statement, Piper said she was delighted to be returning to the show, but that fans would have to "wait and see" what her character did next.
The new doctor has usually been introduced on the show through regeneration, but Piper's statement does not make it clear whether she will be the 16th doctor.
If confirmed as the new Doctor, Piper will be the third woman to have played the role, following Whittaker and Jo Martin.
Piper added: "It's no secret how much I love this show, and I have always said I would love to return to the Whoniverse as I have some of my best memories there, so to be given the opportunity to step back on that Tardis one more time was just something I couldn't refuse, but who, how, why and when, you'll just have to wait and see."
Moments after the series finale aired, Piper shared a series of photos on Instagram, including two selfies of her holding a white rose and two of her playing the character Rose. The caption under the photos read: "A rose is a rose is a rose !!!"
Doctor Who showrunner and head writer Russell T Davies said: "Billie once changed the whole of television, back in 2005, and now she's done it again!
"It's an honour and a hoot to welcome her back to the Tardis, but quite how and why and who is a story yet to be told.
"After 62 years, the Doctor's adventures are only just beginning!"
Piper first appeared in the show in 2005 when it returned to TV for the first time since the 1990s, appearing alongside Christopher Eccleston and then David Tennant.
In a statement, Gatwa said of his departure: "You know when you get cast, at some point you are going to have to hand back that sonic screwdriver and it is all going to come to an end, but nothing quite prepares you for it."
He added: "There are no words to describe what it feels like to be cast as the Doctor, nor are there words to explain what it feels like to be accepted into this iconic role that has existed for over 60 years and is truly loved by so many across the globe."
Gatwa thanked "Whoniverse" fans for "welcoming me in, and making this such a touching experience.
"I've loved every minute of it, but now is the time to hand over the keys to that beloved blue box and let someone else take control and enjoy it every bit as much as I have.
"I'll truly miss it, and forever be grateful to it, and everyone that has played a part in my journey as the Doctor."
