Written and first recorded by Cat Stevens (1966, released 1968).
Hit version by The Tremeloes (US #13/UK #4 1967).
From the wiki: “‘Here Comes My Baby’ was written by Cat Stevens in 1966, and was almost released as Cat’s first single in September 1966. But, ‘I Love My Dog’ was thought to be a stronger song. Even after the success of ‘I Love My Dog’ (UK #28), ‘Here Comes My Baby’ was shelved for several months. The Tremeloes picked it up and it became their breakthrough hit in America and their first hit in the UK after the departure of the group’s lead singer, Brian Poole.
“The Tremeloe’s success with the song helped to establish Cat Stevens as a songwriter (‘Wild World‘, ‘The First Cut is the Deepest‘). His recording of ‘Here Comes My Baby’ was included it on his first album, Matthew And Son, released in 1968.”
The Tremeloes, “Here Comes My Baby” (1967):