Taylor Swift’s Boyfriend Joe Alwyn 'Has Zero Interest in Being a Celebrity': Source

Joe Alwyn isn’t in Hollywood for the fame.

In the new issue of PEOPLE, a source opens up about the actor’s serious, under-wraps romance with Taylor Swift.

“Joe has zero interest in being a celebrity,” a source close to Swift tells PEOPLE. “Their personalities are very compatible, and they’re respectful of each other’s careers.”

Indeed, since they began dating more than two years ago, Alwyn, 28, and Swift, 29, have purposefully kept their relationship out of the spotlight while focusing on their respective work — and supporting one another along the way.

Alwyn was a familiar face in the crowd during Swift’s record-breaking, international Reputation Stadium Tour last year, and she was by his side for the Golden Globes, BAFTAs and Oscars as he supported his critically acclaimed film The Favourite.

In the past, the British actor has opened up about making the choice to keep their romance private.

RELATED: Joe Alwyn Says He and Taylor Swift ‘Have Been Successfully Very Private’ in Their Relationship

“I don’t think anyone you meet on the streets would just spill their guts out to you, therefore why should I?” he told Mr. Porter for a January article. “And then that is defined as being ‘strangely private.’ Fine. But I don’t think it is. I think it’s normal.”

And in a September chat with Total Film, Alwyn said: “I understand people’s curiosity in the world we live in, about people’s private lives. Well, I don’t understand it, but I know it exists. For me, I just don’t feel it’s something I want to offer up to be picked apart by people who don’t know about it, and it’s just not theirs to have.”

The Swift source notes that the privacy has only strengthened their bond.

“Keeping it private from the beginning really helped their relationship,” says the source. “They were able to get to know each other in peace.”

Adds the source: “They have a very special relationship. Joe adores Taylor.”