The show is canonically established to be part of the Prime Universe, but it can be argued that it belongs to both.
The Kelvin Timeline was introduced in the 2009 Star Trek reboot movie, directed by J.J. Abrams and starring Chris Pine as James T. Kirk.
This movie replaced the original cast with new actors, but its twist revealed that it wasn't a traditional reboot, instead creating a new timeline while keeping the previous shows and movies as part of the main canon in another timeline.
The return of Leonard Nimoy as Spock Prime alongside Zachary Quinto's new version of the legendary Vulcan confirmed this.
Author's summary: Exploring Star Trek: Enterprise's timeline.