Temperton died in London last week at the age of 66 after "a brief aggressive battle with cancer", Jon Platt of Warner/Chappell music publishing said.
Temperton's other hits included Off The Wall and Baby Be Mine for Jackson and Boogie Nights for his band Heatwave.
Chic guitarist Nile Rodgers was among those paying tribute, tweeting: "Your genius gave us a funkier world!"
Michael Jackson's sister LaToya wrote: "A brilliant prolific #songwriter Rod Temperton may you #RIP one of my favorite #songs Rock With You #Thriller #legend #Music #MichaelJackson"
Producer and DJ Mark Ronson wrote: "So devastated to hear that Rod Temperton has passed away. a wonderful man & one of my favourite songwriters ever. thank you for the magic x"
Temperton, whose private funeral has taken place, was nicknamed The Invisible Man because of his low profile.
Born in Cleethorpes, North East Lincolnshire, Temperton traced his songwriting ability back to his father's influence.
"My father wasn't the kind of person who would read you a story before you went off to sleep," he once said.
"He used to put a transistor radio in the crib and I would go to sleep listening to Radio Luxembourg, and I think somehow that had an influence."
In the 1970s, after a spell working in a frozen food factory in Grimsby, he answered an advert in Melody Maker magazine for a keyboardist.
The band he joined was disco group Heatwave, and his songs like Boogie Nights, Always & Forever and Groove Line became big hits for the band in the 1970s.
By the time he left the band in 1978, his tunes had caught the attention of producer Quincy Jones, who was looking for songwriters for a new Michael Jackson LP.
Temperton penned three songs for Off The Wall, which became Jackson's breakthrough solo album - the title track, Rock With You and Burn This Disco Out.
He went on to write three more for follow-up Thriller - the title track, which became one of Jackson's signature smashes, plus Baby Be Mine and The Lady in My Life.
They helped make Thriller the best-selling album of all time in the US, with 32 million copies sold.
His tunes have also been recorded by artists including Anita Baker, Donna Summer, Aretha Franklin and The Brothers Johnson.
Temperton won a Grammy Award in 1990 for his work on Birdland, from Quincy Jones's album Back on the Block.
He was nominated for two Oscars in 1986 for his work with Jones on the soundtrack for The Color Purple.
He once summed up his approach to songwriting: "The first criteria is write something you love first, and once you feel those hairs standing up on the back of your hand, you can go to the world."
In a statement released on Wednesday, Warner/Chappell's Jon Platt said: "His family is devastated and request total privacy at this, the saddest of sad times."
Vocalist Chaka Khan, who recorded Temperton's tracks with the funk band Rufus, paid tribute, writing on Twitter: "Thank u 4 your superlative songwriting @RodTemperton. U will always Live in Me. Rest in power."
BBC radio presenter Gilles Peterson wrote: "Apart from Lennon and McCartney no one from the UK has written more gold plated songs than Sir Rod Temperton... a huge loss. RIP"
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Rod Temperton, the British songwriter best known for Michael Jackson's Thriller and Rock With You, has died.