The 37-year-old singer also credited the legendary jazz singer, who died aged 96 on 21 July in his hometown of New York, as her "real true friend".

Despite nearly 60 years between them, Gaga and Bennett collaborated together on several projects, including his final album.

In a lengthy post on Instagram, shared with a picture of the singers hugging one another, Gaga wrote: "I will miss my friend forever. I will miss singing with him, recording with him, talking with him, being on stage together.

"With Tony, I got to live my life in a time warp. Tony and I had this magical power.

"We transported ourselves to another era, modernised the music together, and gave it all new life as a singing duo. But it wasn't an act.

"Our relationship was very real. Sure, he taught me about music, about showbiz life, but he also showed me how to keep my spirits high and my head screwed on straight. 'Straight ahead', he'd say.

"He was an optimist, he believed in quality work and quality life. Plus, there was the gratitude...Tony was always grateful."

In 2014, when Bennett was 88, he broke his own record as the oldest living performer with a number one album on the US Billboard 200 chart for his duet project with Gaga - Cheek To Cheek.

Three years earlier, he had topped the charts with Duets II, which also featured Gaga, as well as the last studio recording of Amy Winehouse.

Bennett's final album in 2021, titled Love For Sale, featured duets with Gaga on the title track, Night And Day and other Cole Porter songs, and won him his last Grammy award.

Bennett retired from performing in 2021 after revealing he had been diagnosed with Alzheimer's in 2016.

Gaga said: "I've been grieving the loss of Tony for a long time. We had a very long and powerful goodbye.

"Though there were five decades between us, he was my friend.

"My real true friend. Our age difference didn't matter - in fact, it gave us each something neither of us had with most people. We were from two different stages in life entirely - inspired.

"Losing Tony to Alzheimer's has been painful but it was also really beautiful. An era of memory loss is such a sacred time in a person's life. There's such a feeling of vulnerability and a desire to preserve dignity.

"All I wanted was for Tony to remember how much I loved him and how grateful I was to have him in my life.

"But, as that faded slowly I knew deep down he was sharing with me the most vulnerable moment in his life that he could - being willing to sing with me when his nature was changing so deeply.

"I'll never forget this experience. I'll never forget Tony Bennett."

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At the end of her post, Gaga offered advice for others with ageing relatives and friends.

She wrote: "If I could say anything to the world about this I would say don't discount your elders, don't leave them behind when things change.

"Don't flinch when you feel sad, just keep going straight ahead, sadness is part of it.

"Take care of your elders and I promise you will learn something special. Maybe even magical.

"And pay attention to silence - some of my musical partner and I's most meaningful exchanges were with no melody at all."