The 23-year-old model and 32-year-old actress were among the stars to mark the occasion Thursday.
Hadid dedicated a series of posts to Swift on Instagram Stories, including a photo of the singer's dad, Scott Swift, doling out snacks.
"In honor of @taylorswift's bday here's a pic of Scott passing out frozen lemonade and pretzels - bc it's possible that these are the ingredients he used to make one of the greatest friends, entertainers, and women this world will ever know!" she wrote.
"cheers to many more years of time spent stargazing, cooking, and celebrating epic friendship (which is why we forgot to take pics this year? lol) and all the adventure, love, and light you deserve," the star wrote.
"thank you for being you, you are a blessing and inspiration to me and so many x @taylorswift happy birthday," she added.
Aldridge posted a tribute to Swift on her own account, writing, "Happy Birthday My Bestest Buddy. Love you so much @taylorswift."
In addition, actress Ruby Rose and model Martha Hunt wished Swift a happy birthday online.
"Happy birthday to the beautiful @taylorswift!!!" Rose wrote on Instagram Stories.
"Happy birthday to this queen @taylorswift! I don't know how you manage to stay so humble and creative while balancing the weight of the world. I learn so much from you. Love you T!" Hunt wrote on her own account.
Swift celebrated her birthday by sharing a teaser for her Netflix concert special. The trailer shows the singer performing in front of thousands of fans on her Reputation tour.