The Outlander actor, 40, beat bigger stars like Tom Hardy, 42, and Idris Elba, 47, in the poll for RadioTimes.com.
Daniel Craig, 52, has filmed his last movie as 007 in No Time To Die, which is set for release later this year after being delayed by the pandemic.
The top five featured Hardy in second place, followed by Henry Cavill, Elba and Tom Hiddleston.
Bloodshot actor Heughan previously revealed that he auditioned for the Bond role 15 years ago.
“I think a lot of actors were seen in the UK,” he told This Morning. “Of course it would be a dream role.”
RadioTimes.com editorial director Tim Glanfield said: “Sam is clearly very popular with fans, and this victory solidifies his position as one of the public favourites for this most coveted of film roles.
“With a host of incredible talent in the frame to take over from Daniel Craig, Sam certainly has some stiff competition – but this big vote of confidence will certainly be something for Bond 26 producers to consider.”
However, former Grantchester star James Norton remains the odds-on favourite to become the next 007 at 6/4, according to the latest numbers from Betfair, despite being tenth in the fan poll.
Richard Madden is close behind with odds of 4/1, with Heughan, Hardy and - somewhat unexpectedly - his Dunkirk co-star Jack Lowden at 6/1.
Craig recently insisted the delayed No Time To Die will be his final Bond film, amid reports the star was considering another outing as 007.
Radio Times readers were asked to vote from a shortlist of 20.
Radio Times' Top 10 Bond replacements poll
1. Sam Heughan
2. Tom Hardy
3. Henry Cavill
4. Idris Elba
5. Tom Hiddleston
6. Richard Madden
7. Michael Fassbender
8. Aidan Turner
9. Cillian Murphy
10. James Norton
With additional reporting by Press Association