Singer Streisand, 83, shared a belated well-wishes message to Friends actress Aniston, who turned 57 earlier this month, on Instagram on Wednesday.
Sharing a throwback photograph of the pair taken at the 30th Annual Screen Actors Guild Awards in 2024, Streisand wrote: "Dear Jen, Wishing you a Happy Belated Birthday. So happy you are happy now! Love, Barbra."
The post appeared to reference Aniston's relationship with Curtis, 50, a life coach and self-described "transformational coach and hypnotherapist".
The couple were recently seen viewing an apartment together in New York's Upper East Side, in what was reported to be a further sign of their commitment.
Curtis has placed his $US1.5 million ($A2.1 million) Manhattan property on the market.
Earlier this month, Aniston and Curtis marked their first Valentine's Day together.
Aniston shared a photograph of a box of Sweethearts candy in her hand, with Curtis visible in the background. The couple made their relationship Instagram official in November when Curtis celebrated his 50th birthday.
Curtis addressed their relationship during an appearance on the Today show last month, where he was promoting his forthcoming book, The Book of Possibility, due for release in September.
Asked how they met, Curtis said: "We were introduced by friends."
He added: "We found out that we had mutual friends and we started to just chat.
"It took a long time, but we chatted for a long time and became close."
Today co-host Craig Melvin asked: "How's it going? How long have you guys been hanging out?"
Curtis replied: "A long time, months now. Close to a year."
When Melvin observed: "You're kind of blushing right now," Curtis responded: "I sure am."
Aniston has largely kept her relationship with Curtis private, but in an interview with Elle in November she spoke about his work.
She said: "Hypnotism is one of the many things that he does. He's quite extraordinary, and helps many, many people.
"He's very special, very normal, and very kind, and wants to help people heal, move through their trauma and stagnation into clarity. It's a beautiful thing to commit your life to."
Curtis supported Aniston at the season three premiere of her Apple TV+ drama The Morning Show in September.
Aniston was previously married to Brad Pitt, 62, from 2000 until 2005, and Justin Theroux, 54, from 2011 until 2017.
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