"Two of the very favorite women in my life. You keep my heart swelling and healthy, @alainamariemeyer and @thesaragilbert," he wrote.
"The Big Bang Theory" was nominated for three awards, The Show of 2018, The Comedy Show of 2018 and The Comedy TV Star of 2018 for Galecki's co-star Jim Parsons.
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Parsons won in his category.
Galecki and Meyer went public with their romance in September. Galecki attended Meyer's sister's wedding the next month.
"What a wonderful wedding @meri_meri @ericdehner with such amazing humans. My sister is married and it was so beautiful. Our family just doubled in size and I couldn't be happier #itsdehnertime," Meyer captioned a photo on Instagram.
Galecki plays Leonard Hofstadter on "The Big Bang Theory," which is in the midst of its 12th and final season on CBS.
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