Gigi Hadid has finally made her relationship with Bradley Cooper Instagram official

The series of black and white photographs, which were taken by photographer Benjamin Rosser, included a number of Gigi posing with her friends at her party, one of her holding the hand of her four-year-old daughter Khai - who she has with former partner Zayn Malik - and one of her kissing Bradley, 50, with her hands on his face as they stood in front of her three-tier chocolate birthday cake.

Gigi, who turned 30 on 23 April, accompanied the photos with a caption of how "lucky" she feels.

She wrote: "I feel so lucky to be 30! I feel so lucky for every high and low - for all the lessons and gifts both have brought me. To get to feel it all! I'm so lucky to be a mom, friend, partner, sister, daughter, colleague to some of the most unbelievable humans!!

"So lucky for the support and encouragement from all of YOU around the world, every day and on my birthday last week.

"I had the best time celebrating, and it's a blessing to feel so loved!! I am grateful and honored to take on a new decade.(sic)"

In March, Gigi admitted she felt "really lucky" to have found the 50-year-old actor - who has daughter Lea, seven, from his relationship with Irina Shayk -and explained that he is always "encouraging" her to strive within her career.

She told Vogue magazine: "I think just getting to the point where knowing what you want and deserve in a relationship is essential and then to find someone that is in a place in their life where they know what they want and deserve...and you both do work separately to come together and be the best partner that you can be. I just feel really lucky. Yeah, lucky's the word.

"I respect him so much as a creative and I feel that he gives so much to me: encouragement and, just, belief. For those people you admire to encourage you, it can create so much belief in yourself. Like, what's the worst thing if I auditioned for this? You jump and take the leap."

And the model admitted they were trying to have a "normal" personal life, but being in the public eye made it difficult.

She said: "Bradley has opened me up to going to the theatre more, and that's something that's so nice to bring back into my life.

"You want to give yourself a normal experience of dating and even for my friends who aren't public figures, that's hard. Where do you go? And, what? You just start talking to people?

"And then there's another added layer of privacy and security. You want to believe that people are going to have your back and not call TMZ or go on Deuxmoi or whatever, but you just don't know."