Page said she had suffered for years because of having to hide her sexuality while in the public eye.
"My spirit suffered, my mental health suffered and my relationships suffered," she said. "And I'm standing here today, with all of you, on the other side of all that pain."
The Human Rights Campaign, a lesbian, gay, bisexual and transgender advocacy group that posted her speech on its website, congratulated Page for completing the "deeply personal and arduous journey" of coming out.
Page later took to Twitter to thank the group for their support.
Thank you @HRC and everyone for all the love and support. X
The actress mentioned gay musicians Tegan and Sara Quin and transgender actress Laverne Cox as examples of courage, and hailed American football star Michael Sam who recently came out as gay as a "hero".
Page concluded her emotional speech by thanking the audience for "inspiring" her and giving her hope.
"Thank you. Thank for inspiring me. Thank you for giving me hope, and please keep changing the world for people like me."
- Independent