Kane, 30, revealed that the latest addition to his family would be named Henry Edward Kane.
Messages of congratulation flooded in from other celebrities on Kane’s social media post after the happy news.
“Welcome to the world Henry Edward Kane. 20/8/2023,” he wrote, adding: “Love you baby boy!”
Fomer Tottenham Hotspur hero Kane scored and assisted for Bayern Munich on his Bundesliga debut against Werder Bremen in a 4-0 victory on Saturday.
He departed boyhood club Spurs for an initial £100million fee, which could rise to £120m with add-ons.
Kane’s move to Germany had been complicated by the fact his wife Kate was heavily pregnant with their fourth child which means in theory it could have played for either rival side.
She returned to London last Monday with the rest of their young family. Kane said a decision will be made on where she gives birth.
“My wife Kate was really supportive, she wants the best for me and my career so she said to push, she wants me to be playing and happy and that is why we made the decision,” Kane added.