The 35-year-old actor joined the picture-sharing site last week but took a few days to start following his 26-year-old girlfriend.
Meanwhile, in a new interview, Tom has praised musicians for their emotional vulnerability.
The star did not mention his singer/songwriter girlfriend directly but said musicians and singers have it more difficult than actors because they share their most personal thoughts and feelings in their music.
Speaking at a SAG-AFTRA Q&A in Los Angeles, Tom said: "I really have such respect for musicians and for singers because they're so naked. Actors get to hide behind character, even though we're really expressing ourselves, but people don't tell that.
"But musical performers are up there and it's them. I have a guitar and this is the song I wrote, this is how I feel. But the power you have to make people feel good is extraordinary and that's the reason why these performers are unstoppable."
Tom and Taylor have been dating since June but the actor was previously forced to deny claims his relationship with the star is a "publicity stunt".
He said: "Well, um. How best to put this? That notion is - look, the truth is that Taylor Swift and I are together and we're very happy. Thanks for asking. That's the truth. It's not a publicity stunt."
And the 'Thor: Ragnarok' star recently insisted he doesn't care what people think of his relationship because he knows he's being "authentic" and true to himself.
When asked if the focus on his personal life annoys him, he said: "I don't know, it comes down to being authentic.
"Everything you do you have to make sure you truly believe in it and as long as you know that, it doesn't matter what anyone else says about it because the nature of being a public figure is that everyone will have an opinion about anything you do, and as long as you know why you've done something and you've committed to it with authenticity then you're OK."