Beckford moved to Everton on a free transfer on Monday and boss Simon Grayson has immediately snapped up Paynter, who hit 29 goals for the Robins last season as they chased Leeds for promotion to the Championship.
The former Bradford and Southend striker has signed a three-year deal at Elland Road.
Leeds gained automatic promotion but Swindon missed out in the Play-off final to Millwall. But the 26-year-old Paynter was a constant thorn in most teams' sides last year, even scoring four goals against Grayson's men.
Grayson told his club's official website: "He proved his worth last season, scoring four goals against us in two games. He has matured as a player over the last couple of years and he had a fantastic season last season.
"He works ever so hard, holds the ball up well and he has proved he knows where the back of the net is. When we knew he was available we were desperate to get him. We feel he will be a good acquisition for the club and I am delighted to have got him," he added.
"I've said before that whenever we sign a striker, people will link him to Jermaine but he is not Jermaine Beckford he is Billy Paynter.
"He has got a different style about him and he will do the things that brought him success last year. Jermaine has his strengths and weaknesses and Billy will have as well.
"There will be comparison and Jermaine Beckford was something different at times. But some of Billy's strengths were better than Jermaine's and maybe some of Jermaine's strengths were better than Billy's. That's why you can't really compare people.
"He was a constant threat to us, and not just because of the goals he scored against us but in terms of his hold up play, his work rate and movement. He caused us a lot of problems. We have gone out to get a player we think will positively affect us."
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