Inside Taylor Swift and Tom Hiddleston's Whirlwind Romance: 'They've Fallen for Each Other Very Quickly,' Says Source

"Normally, Taylor is very reserved and private, but she's totally open and happy with Tom," says a source

Photo: INFphoto

Between cuddling up on beach dates, meeting the parents and traveling Europe together, Taylor Swift and Tom Hiddleston‘s picturesque romance has been a whirlwind.

And though the “Shake It Off” singer only split from deejay Calvin Harris weeks before she first stepped out publicly with the Crimson Peak actor, a source tells PEOPLE exclusively the new couple is going strong.

“They have fallen for each other very quickly,” says the source. “They’re very close for people who have only been dating for a couple of weeks.”

Indeed, a Hiddleston family source told PEOPLE the actor’s mom couldn’t stop gushing about Swift after spending the weekend with her.

“She thinks Taylor is the loveliest,” says the family source. “She was so happy to meet her. Taylor was almost immediately part of the family.”

For more on Taylor Swift and Tom Hiddleston’s whirlwind romance, pick up the latest issue of PEOPLE, on newsstands Friday.

Swift, 26, was single for two years before her 15-month-long relationship with Harris, 32, and was open about stepping away from the dating scene after her dating life became “a bit of a national pastime,” she told Rolling Stone.

But Hiddleston, 35 – who traveled to Rome with Swift after their family weekend in England – appears to have won over the singer.

“Normally, Taylor is very reserved and private, but she is totally open and happy with Tom,” says the source.