Taylor Swift 'Is Very Happy' with Boyfriend Joe Alwyn, Says Source: 'He Is Her Rock'

Taylor Swift and boyfriend Joe Alywn's "Love Story" is going strong.

In this week's issue of PEOPLE, on newsstands Friday, a source close to the superstar, 31, says she "is very happy" with the British actor, 29, whom she has dated for more than four years.

"He is her rock," says the source. "Their relationship is mature and wonderful."

While the source says that Swift "loves" that she and Alwyn "have been able to keep their relationship so private" since they started dating in 2016, the singer has been more open about him in recent months.

"I think that in knowing him and being in the relationship I am in now, I have definitely made decisions that have made my life feel more like a real life and less like just a story line to be commented on," Swift told Paul McCartney in December during an interview for Rolling Stone. "Whether that’s deciding where to live, who to hang out with, when to not take a picture ... it’s really just trying to find bits of normalcy."

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Quarantining together amid the pandemic, the couple bonded even further by cowriting songs. After months of speculation, Swift confirmed in her Disney+ documentary Folklore: The Long Pond Studio Sessions, which premiered in November, that "William Bowery" — the mystery songwriter on her Grammy-nominated surprise summer album folklore — is, in fact, Alwyn.

"I heard Joe singing the entire fully formed chorus of ‘Betty’ from another room, and I just was like, 'Hello,'" Swift revealed in the film about the folklore track. "I came in and I was like, 'Hey, this could be really weird and we could hate this, [but] because we’re in quarantine and there’s nothing else going on, could we just try to see what it’s like if we write this song together?'"

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Swift has since teamed up with Alwyn for three more songs on her new album evermore, which dropped as a surprise for fans on Dec. 11. On the record, Alwyn (under his "William Bowery" pseudonym) is credited as a co-writer on three songs — "Champagne Problems," "Coney Island" and evermore’s title track — but is happy to stay behind the scenes.

"Taylor was very excited to share a second album with fans, and Joe has been supportive as always," the source says. "He is a very laidback person."

In 2021, Swift likely won't be slowing down, as she's nominated for six Grammys at the annual awards ceremony being held on Jan. 31. But first, says the source, she and Alwyn "are looking forward to celebrating Christmas together."

For all the details on Taylor Swift's private world, pick up the latest issue of PEOPLE, on newsstands Friday.