The Something Borrowed star, who guest starred on Glee as dance teacher Cassandra July, offered up her home to the Glee star when Michele needed to escape from the public eye.
"I called [Kate Hudson] and said, ‘I don't know where I'm going to go because my house is swarmed [with reporters],'" Michele told Elle. "She was like, ‘Oh, you're going to stay at my house.' Like it was nothing. No one knew I was there. I'll never really be able to thank her, truly, for what she did for me."
The 27-year-old actress covers the mag for its December issue, looking stunning in smoky eye make-up, a white belted jacket and denim jeans with a chain waist belt.
Michele not only opened up about Hudson's support during that time, but also how she has taken time to heal and cope.
"I never thought I would be in this position in my whole life," Michele continued. "Now that I am in this position, you can choose to rise, and that's what I'm going to try to do. I know that Cory would want nothing more than for me to take this situation and use it to help people."
To the shock of friends, family and fans, Monteith was found dead in his room at the Fairmont Pacific Hotel in Vancouver in July. He passed away from a drug overdose, officially referred to as mixed drug toxicity.
Following his death, Michele said little about Monteith's passing until she opened up to TV Week Australia in October, saying, "I really woke up every single day feeling like I was being in some sort of spell or something, that I was lucky enough to have him in my life. I feel like what happened with [Monteith's death] was [miniscule] in the scheme of who he was and his life."
"There was no greater man than Cory," she added, "so for the time we spent together I consider myself very lucky."
Michele and Monteith started dating at the beginning of 2012, after she split from her longtime boyfriend Theo Stockman.
Elle's December issue hits newsstands Nov. 19.