"G'day Aussies," she began in the letter read out on ABC's 7.30 program on Thursday by her partner Nick Coyle.
"This is a love letter to 25 million people and seven million square kilometres of land.
"Land abundant in nature, beauty and space.
"It is not the same in here.
"I haven't seen a tree in three years."
Ms Cheng was working as a journalist in China when she was arrested in 2020 on suspicion of illegally supplying state secrets overseas.
Since then, the former Chinese state media anchor has not seen or spoken to her two children.
Last year she faced a closed trial in Beijing on national security charges.
The outcome of that trial is not known.
Mr Coyle said Ms Cheng was making her statement now after years of public silence because three years was a "very poignant" milestone.
Her daughter is now in high school and her son will go to high school next year.
In the letter, Ms Cheng said she missed many things but her children most of all.
"I miss the sun," she said.
"In my cell, the sun shines through the window, but I can stand in it for 10 hours a year," she said.
"Every year the bedding is taken into the sun for two hours to air.
"When I came back last time, I wrapped myself in the doona and pretended I was being hugged by my family under the sun.
"I can't believe I used to avoid the sun when I was back in Australia ..."
Mr Coyle described Ms Cheng as a person who was funny, very determined, very smart and full of life.
But her separation from her children was taking a toll.
"Yeah, we all miss her deeply," he said.
"She would no doubt go through very, very difficult times.
"She only gets a window to the outside world for 30 minutes once a month through the consular visits and when she writes to me, she is full of optimism because that's her nature."
Foreign Affairs Minister Penny Wong has previously raised concerns about Ms Cheng's detention, as had her coalition predecessor Marise Payne.
"The Australian government has advocated at every opportunity for Ms Cheng to be reunited with her family," Senator Wong said in March.
"Australia has consistently called for Ms Cheng to be afforded basic standards of justice, procedural fairness and humane treatment in accordance with international norms.
"We will continue to provide consular support to Ms Cheng and her family, and to advocate for her interests and wellbeing."
So far, China has said Australia should stop interfering in the case.
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