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The record was previously held by Bill Anderson, who won the honour in 1960 at the age of 23, and Johnny Cash, who won in 1956 when he was 24 years old.
Swift also scored her third consecutive BMI Country Song of the Year title for her hit track You Belong With Me, making her the first songwriter to win the prize three years in a row.
The Love Story hitmaker took to the stage and paid tribute to a close friend, whose funeral she attended just 24 hours earlier, telling the crowd, "It’s been a really emotional week."
Billy Sherill was named BMI icon at the ceremony and a host of country stars including Ronnie Dunn, George Strait, Martina McBride and Faith Hill paid tribute to the record producer.
Other songwriters honoured at the ceremony in Nashville, Tennessee included Keith Urban, Toby Keith, Miranda Lambert, Sugarland's Kristian Bush and Dave Haywood and Charles Kelley of Lady Antebellum.