The actress, who plays the lead role of Meredith Grey, made the comments while picking up an award for 'Favourite Dramatic TV Actress' at last night's People's Choice Awards.
"Thank you so, so much for this," Pompeo, wearing Lanvin, said.
"We've been doing this show for nine seasons and it feels like an eternity, and to have this warm a reception and to be getting awards nine seasons later - I share Katy Perry's sentiment, we have the best fans in the world."
Pompeo, who said that she "really can't thank" the fans enough, added that the best part of being on the show is interacting with viewers.
"After nine seasons, definitely my favourite moments have been looking in your eyes and seeing your smiles and seeing your faces light up when you see us on the street or wherever we are," she said.
"Hearing your stories, whether they're heartbreaking or hilarious. The fans of this show have truly touched me in ways I never thought possible, so for that I am forever grateful, and I love you dearly. Thank you so much."
Grey's Anatomy airs Thursdays on ABC.
Photo gallery - People's Choice Awards 2013 red carpet:
Copyright: WENN Adriana M Barraza