Ms Amin said: “If not for Israel, I don't know what would have happened. Israel truly believes in human rights. Thank you. You saved me.”
Ms Amin is a regular contributor to the newspaper’s Persian site, and has worked on a freelance basis.
Her work for the Times of Israel was reportedly a factor in her potential deportation from Turkey.
Ms Amin, who left Iran for Turkey in 2014, had previously appealed to the United Nations and other human rights organisations for protection.
The UN Watch NGO recently circulated a petition on her behalf, saying she was in “grave danger should she be deported back to Iran”.
Mr Horovitz said he was “proud” of his country for acting so quickly in assisting his colleague, saying officials had been “helpful and professional”.