Walcott wrote the letter to Edward Herdman and his partner Emma to pass on his condolences following the death of their son Theo, who was named after the Arsenal winger.
The England international and father of two used letter to pass on both his sympathies and those of his club.
The letter read: "Dear Emma and Edward, it was with great sadness that we learned recently of the passing of your baby son Theo.
"On behalf of us all at Arsenal Football Club, we extend to you our very sincere condolences. As a father of two young children myself, I cannot begin to imagine how you both must be feeling at this time.
"My heart goes out to you and everyone close to you.
"I know that the feelings you have for Theo will stay with you all forever, and be proud that you are loving parents to this most wonderful child.
"I feel very honoured to learn that I had an influence in you naming your son Theo. This is very touching for me. My thoughts are with you both.
"Stay strong and remain very proud of yourselves. I am in utter admiration of you both.
"With very best wishes, Theo Walcott."
Edward Herdman took to Twitter to praise the player and club for the gesture.
Thank you so much @Arsenal & @theowalcott for this incredible letter regarding my son who we lost earlier this year. Such a class club. #afc pic.twitter.com/rvrPFTcW4v
— Edward Herdman (@edherdman14) 6 September 2017