The song is in C major. The “circle of fifths” progression popular in pop music is not used in this song. But, like other pop songs, the chord progression is repetitive, meaning the same progression repeats throughout the song.
The verse progression is as follows:
I V vi IV I V IV I
In C major, this would be:
C G Am F C G F C
The chorus changes the first four chords:
vi vi/V IV I I V IV I
In C major, this would be:
Am Am/G F C C G F C
There are some small changes and transition notes, such as the ones in the second-to-last phrase: When going from the F to the C chord, the transition goes F C/E G/D C. (Ex: Here, 35 seconds in) See how the bass notes are all in order—F, E, D, C. A common practice in music is to connect the bass notes, generally when in root position, with notes in between.