Caitlyn Jenner cuddles her grandson Bodhi and is one happy grandmother - Daily Mail

Caitlyn Jenner was one happy grandmother as she cuddled her newborn grandson on Sunday.

The former Olympian shared an image of herself holding the child - the firstborn of her oldest son Burt and his long-term partner Valerie Pitalo. 

'So excited for Burt and Valerie,' Caitlyn wrote on Instagram. 'They named their adorable first child Bodhi. The first Jenner boy!! the name moves on :)'

'The first Jenner boy!' Caitlyn Jenner is one happy grandmother as she cuddles her 'adorable' newborn grandson Bodhi

The infant son's middle name is Burton, the full first name of his father.

Burt himself was named in honour of Caitlyn's younger brother, who died aged just 18 in a car crash.

The racing car driver posed with Caitlyn and Bodhi in the snap.

The 37-year-old has himself been active on social media following Bohdi's birth. picture of the baby snuggling into his mother's chest soon after birth.

'She did it,' Burt Jenner has announced the safe arrival of a baby boy with girlfriend Valerie Pitalo by sharing an Instagram snap of the pair

A second image shared the sleeping child, wrapped in the ubiquitous striped hat and footprint blanket of U.S. maternity hospitals, cradled by a recovering Valerie.

Jokingly, the 37-year-old captioned the second image: 'So far so easy... Only 17 years 364 days to go!'

The baby is a first child for Burt, who has five siblings and is stepbrother to the Kardashian clan.

His younger sister Casey Jenner is already a mother-of-two daughters, and the 35-year-old is currently pregnant with a son.

'So far so good': A second image shared the sleeping child, wrapped in the ubiquitous striped hat and footprint blanket of U.S. maternity hospitals, cradled by a recovering Valerie

His brother Brandon Jenner welcomed daughter Eva James a year ago, his first child with wife Leah.

Burt and Valerie announced their happy news via Instagram last year.

'I promised to wait until we had the "all healthy" update, and we got it yesterday,' Burt said, sharing an image of their son's sonogram.

Proud parents: Long-term couple Valerie and Burt are pictured in an Instagram snap

Close: Burt with his parent Caitlyn Jenner; he has been a steadfast supporter of the former Olympian

'My Lil boy, just chillin... So happy I can't see straight, he can't get here fast enough... Who wants to fab me a stroller with @kingshocks and @gladiatortires like you see at the 1000 every year?' he added.

Caitlyn has been spending more time with Burt ever since Bruce split with Kris Jenner, 60, in 2014.

And the sports lover has been by Bruce's side as he became Caitlyn.

Burt was there when the champ talked to Diane Sawyer this spring.

And Burt posted a photo of Caitlyn in September via Instagram, writing, 'Yup all you haters, my dad will still probably whip your ass at 65 with implants.' 

Part of the clan: Burt is seen as a child, front and center, with his siblings and Kardashian step-siblings