Peirson will join the tour ahead of the second Test at Lord's with Inglis due to return home for birth of his first child. Inglis will return to the squad at a later date.
Peirson's call-up is reward for three very consistent Sheffield Shield seasons - since the start of the 2020-21 campaign he has made 1337 runs at 37.13 with five hundreds.
He has also represented Australia A on two tours, making an unbeaten century in Sri Lanka last year. He has also trained with the main squad in recent weeks.
"Obviously there's an away Ashes next summer. I'd love to get over and play some sort of cricket in England," he said. "I've played premier league cricket quite a few years ago now but would love to experience those conditions again and develop my game.
"If I don't play Test cricket that would be a frustration, but all I can do is when I'm done, sit in my armchair and know that I did everything I could."
The bulk of Australia's squad departs for the UK on Friday ahead of the World Test Championship final against India on June 7. They will spend a few days in the north west of England before relocating to London to begin training.