The singer shared rare insight into her relationship with the businessman in her new Vogue cover story ... explaining all about their initial meeting and instant connection.

Per the pop star, her mother, Cynthia Germanotta, put Michael on her radar after crossing paths with him amid shared philanthropic efforts ... telling Gaga she "just met your husband."

While Gaga was wary about pursuing Michael at first, she orchestrated their meeting at Sean Parker's birthday party in September 2019 ... where they instantly hit it off and talked for 3 hours.

Michael expressed a similar first impression to Vogue, saying he was "struck immediately by her warmth and openness."

After staying in contact on the phone for weeks, they eventually went on their first date ... which led to them quarantining together in Malibu during the pandemic.

Gaga credited the private time together as a win for their relationship ... as it allowed her to "completely focus" on their growing romance without career distractions.

She added ... "I met this totally supportive, loving human being who wanted to get to know me -- outside of Lady Gaga.”

Michael proposed to Gaga back in April, after a day spent rock-climbing ... though, the pair kept their relationship update private for several months.

The singer appeared to confirm the engagement during the Paris Olympics ... when she proudly referred to Michael as her "fiancé."

This is Gaga's 3rd engagement -- she was previously connected to actor Taylor Kinney, and talent manager Christian Carino -- she's making it clear she's heading to the altar with Michael ... saying they're "right for each other."

Michael and Gaga aren't just putting their love on display in Vogue ... they're also showing out at the Venice Film Festival -- where the singer opened up about the drastic physical transformation she undertook for her role in "Joker: Folie à Deux."