He posted a video to coincide with Father's Day, which was celebrated in the US on June 19, which included clips of Robert spending time with his father when he was a young child.
Steve, known as the Crocodile Hunter, tragically died in 2006 when a stingray barb pierced his chest while filming an underwater documentary. Robert and his sister Bindi were aged just two and eight respectively.
In the emotional video posted to TikTok, Robert is seen hugging his father, sitting on his shoulders and being taught how to hold a lizard as a young toddler.
"I had the best dad in the world," Robert captioned the video.
"Thinking of him and remembering nothing but fun times. I hope you all had a wonderful Father's Day in the US – sending love to those who couldn't celebrate with their dad."
In a separate post on Instagram, Robert said Father's Day was a day "filled with emotion".
"I think of my dad a lot and remember him fondly. But now, I also think about and admire my brother-in-law Chandler and what a fantastic father he is to my niece, Grace. I am so happy that she has such a fun and kind person to help guide her through life," he said.
Bindi commented, "This is the sweetest", while her husband Chandler Powell was equally touched by the message.
"Thanks Robert. Love our adventures together and now Grace gets to join in on them! Glad that Grace has such an awesome Funcle. Thanks for being the best brother-in-law," he said.
Fans praised Robert for the sweet tribute to Steve, with one saying he was an "absolute legend".
"He was a dad to anyone who didn’t have a father to take them on adventures as a kid and taught some of us how to be brave when encountering wild animals," one wrote.
"I’m absolutely bawling," another said.
"You remind me so much of him. When I listen to you talk about conservation it’s like listening to him," a third responded.
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