Taylor Swift and Travis Kelce are enjoying their newly engaged glow.

“Taylor and Travis have been in celebration mode ever since the engagement,” a source close to the couple tells PEOPLE. “They are not in the wedding planning phase yet.”

Nearly two years after making their romance public, the Grammy winner and the NFL star, both 35, announced their engagement news in a joint Instagram post on Aug. 26.

“Right now they just want to enjoy being engaged and they are going to take their time with it,” the source adds. “It has been a relief not having to keep it a secret anymore, and they are glad it is out in the open.”

“Your English teacher and your gym teacher are getting married 🧨,” the pair wrote in their announcement, ending the caption with a dynamite emoji, seemingly a reference to their “TNT” nickname.

The couple also shared a carousel of photos from the moment the Kansas City Chiefs tight end popped the question in his backyard — surrounded by a stunning floral arrangement — two weeks before revealing the engagement.

“They were going out to dinner and she was ready to go and he said, ‘Let’s go out in the garden on the patio and have a glass of wine before we go,’” Kelce’s dad Ed said on Australian radio’s The Jimmy & Nath Show with Emma. “I think she knew something was up because as they walked out there, she could see, suddenly, there were a lot more flowers out there.”

Ed added: “These are two young people madly in love with each other, and I think this is great.”

The source close to the couple previously told PEOPLE that “both families are overjoyed. There were toasts, happy tears and everyone is thrilled for them.”

Kelce’s mother Donna has been holding onto keepsakes from the milestone moment.

“Donna is already saving little things from this time like photos, notes and flowers,” the source told PEOPLE. “She is very sentimental about it. She wants to remember every detail, so she has been holding onto mementos from their first days as an engaged couple.”

The engagement news came just weeks after Swift appeared on the New Heights podcast — which Kelce hosts with his brother Jason — to announce that her new album, The Life of a Showgirl, will drop on Oct. 3.