The former King in the North has Targaryen blood flowing through his veins — his mother is Lyanna Stark and his father is Rhaegar Targaryen. (Something Sam finally fills Jon in about in the premiere, FYI.) Like Dany, Jon appears to have a similar bond with the dragons as opposed to a magical control over them. They must be able to sense both his Targaryen blood and his relationship with their mother.
We previously got a glimpse of how the dragons would react to Jon climbing aboard in the season seven episode "Eastwatch," when Drogon allows him to get close and even stroke his scaly skin while on a cliff in Dragonstone. In the premiere, Jon not only gives Rhaegal a few pats, but also climbs up after Dany tells him to, and the pair fly off to a romantic, icy waterfall in nearby Winterfell. (Anyone else get Aladdin and Jasmine vibes during that scene? No? Just me?)