Mr Perry played Chandler in all 234 episodes of the iconic New York City-based sitcom Friends, which ran for 10 series from 1994 to 2004.
The sitcom catapulted him, Ms Anitson and their four other co-stars to household fame and by its final series saw the group paid more than £800,000 ($1 million) per episode.
But Mr Perry struggled with drug and alcohol addiction for much of his adult life.
In a 2021 memoir he said he had attended 6,000 Alcoholics Anonymous meetings, been to rehab 15 times and had 14 stomach surgeries.
He added that his alcoholism meant drinking 14 triple vodka shots was not enough to get him drunk.
“Not only do I have the disease, but I also have it bad,” he wrote.
“I have it as bad as you can have it, in fact. It’s back-to-the-wall time all the time. It’s going to kill me.”
Ms Aniston said the outpouring of tributes to Mr Perry in the wake of his death was “so beautiful”.
“I hope he can know that he was loved in a way he never thought he was,” she said.