Link studied at the Wharton School of Business but was already publishing songs by his late teens; in 1914, he co-wrote "Along Came Ruth" with Irving Berlin.
In 1929, he co-wrote "I've Got a Feeling I'm Falling" with Billy Rose and Fats Waller.
Waller turned the song into a hit; Louis Armstrong recorded the tune, as did many others.
Among their songwriting credits (often in tandem with other writers) are "By My Side", "Until We Meet Again Sweetheart", and "Peelin' the Peach".
In 1936 he wrote "These Foolish Things" along with Jack Strachey and Eric Maschwitz, which became one of the year's biggest numbers; hit versions include one by Benny Goodman and another by Teddy Wilson and Billie Holiday.