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It was Petty's collaborator Jeff Lynne who noticed the songs sounded alike. The agreement was said to be "amicable."
Sam's rep said in a statement to Billboard, "Not previously familiar with the 1989 Petty/Lynne song, the writers of Stay With Me listened to I Won't Back Down and acknowledged the similarity.
"Although the likeness was a complete coincidence, all involved came to an immediate and amicable agreement in which Tom Petty and Jeff Lynne are now credited as co-writers of Stay With Me."
Tom Petty And The Heartbreakers' song I Won't Back Down:
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Smith has yet to comment on the agreement, but he did seem to allude to Stern's critical remarks via Twitter.
The hitmaker wrote to his 1.62m followers: "Can't believe what I've just read."
Then minutes later, Sam appeared to take the high road on the matter as he shared the simple message: "Ignore."
Sam Smith's Stay With Me mashed-up Tom Petty's I Won't Back Down:
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While doing a countdown of the radio's top songs last week, the 61-year-old radio personality began to discuss Smith and his success.
Stern said: "You know what I like about the guy? He's an ugly motherf*****. He's fat.
"Is he gay? You know what, he looks gay to me, not that anybody looks gay, but he does seem effeminate."
The longtime radio host continued: "I like that he's chubby and gay. That's why I love him. He's one of those guys I feel like, he's really good but I feel like that will be his only hit song.
"That's how good that song is. He's fat and he's gay and little girls worship him. That's when you know you have a good song and you have a good voice."
Stern goes on to mimic Smith's voice by singing along to I'm Not The Only One in a ridiculous falsetto and followed up by saying: "I'd like to get him in here to congratulate him on beating the odds. He's like the male Adele."
The British singer seems to have taken the remarks about his weight to heart as he posted a couple shots of him spending time at the gym.
Smith proudly showed off a grey shirt with sweat stains all over it in what looked to be a fitness room along with the caption: "Werk."
In the other photo he looks amazed as one of his female friends did an advanced yoga position with her legs completely over her head.
- Daily Mail