Walcott spent the last three years of his career at boyhood club Southampton but departed when they suffered relegation last season and his contract expired.
Walcott spent 12 years of his career at Arsenal, where he made 397 appearances, scored 108 goals and won the FA Cup three times.
He also played for Everton and won 47 caps for the England national team, scoring eight goals.
At 17, Walcott was the youngest player at the 2006 FIFA World Cup in Germany.
In an emotional video posted on social media, Walcott said: "The first moment I put my football boots on aged 10 was a special journey for me. From playing in the park with friends to performing in some of the biggest stadiums in front of huge crowds across the world.
"The support shown to me throughout this time has been incredible and in every way imaginable I am truly grateful. I shared the football pitch with so many incredible players and we have created so many unforgettable memories.
"I'd like to say a big thank you to all the managers and coaches that I've worked with, especially Harry [Redknapp] for giving me a start and Arsene [Wenger] for showing the belief and supporting me when I joined the club at only 16 years old. Over 18 fantastic years in the Premier League, there are so many moments I will cherish.
"The early days at Southampton Football Club, my transfer to Arsenal where I spent 12 enjoyable years and scored over 100 goals, winning the FA Cup and scoring in the final which is every kid's dream. To have had the opportunity to represent England 47 times and to go to the World Cup in 2006 aged just 17 and still to hold the record for the youngest-ever debut by a senior England player and the youngest hat-trick goalscorer at 19 - I will never forget that feeling.
"I'm lucky enough to have had offers to continue playing but it feels right to finish where I started and hang up my football boots. Thank you to everyone who has been with me along the way."
