The 33-year-old Nigerian defender has left Ibrox after his contract expired at the end of the 2021-22 campaign.
Balogun joined Rangers in 2020 and won the Premiership and Scottish Cup, as well as reaching the Europa League final.
"Took me some time, but eventually it is time for me to say goodbye,” wrote Balogun via Instagram.
"Thank you to every single soul at the club working their socks of, making sure me and the boys can focus on performing at our best.
"A lot of whom we work with on a daily basis: kitchen staff, medical staff, sports scientists and athletic trainers, as well as our two girls Katy and Hannah. You have shown and taught me – in your very own way - the dedication that is expected and I thank your for that.
"Thank you to the managing staff and especially to my amazing team mates over the two seasons, who welcomed me from day one as a player and a friend. Who have pushed me to be better and taught me the Rangers way.
"A lot of highs, a few lows that made our bond even stronger. We became invincible champions, the class of 55 … those magical European nights at Ibrox that led us all the way to the final. And eventually we crowned my time at the club with the Scottish cup.
"Thanks for all the memories, the laughter and for sharing some of the best moments in my career with me.
"And last but not least, a massive thank you to you, the supporters. You are one crazy, passionate bunch. High expectations, that can be intimidating at times - but I loved every single second of it.
"All your messages over the past two weeks have been incredibly overwhelming for me and at the same time they’re the greatest testimonial I can get for my time at Rangers. It has been an absolute privilege and honour to represent you near and far.
"One of the most frequent questions I’ve been asked in my time at Rangers was if I understand the size of the club and what it means – thanks to you, I do now.
"We are the people and you are my people – Forever Blue."