The couple, who are already parents to 15-month-old son Noah, welcomed their second son on 12 February.
The unusual moniker, which was revealed by TMZ, means the "understanding possessed by Buddha" in regards to the "nature of things" in Buddhism. When translated into English, it can mean simply, "enlightenment".
Megan and Brian are the second set of parents in just a few days to name their baby Bodhi. Australian actress Teresa Palmer and her husband Mark Webber announced the birth and name of their firstborn on Monday – Bodhi Rain Palmer.
Megan, 27, is also a stepmother to Brian's 11-year-old son Kassius with his ex-partner Vanessa Marcil.
In November, the Transformers actress spoke to People about her growing family. "I think Noah is going to be an amazing big brother with time," the star said.
"I think he has an idea, but I don't think he understands that a baby will be living with us all of the time - that will be an adjustment.
"He loves to be the centre of attention," she added. "And I also think he is a really sensitive child. I think that he's going to be a nurturer."
Both Megan and Brian, 40, are notoriously private about their personal life. When she gave birth to her first son in September 2012, they kept the news a secret for two weeks.
"We are humbled to have the opportunity to call ourselves parents of this beautiful soul, and I am forever grateful to God for allowing me to know this kind of boundless, immaculate love," Megan eventually announced in a Facebook post at the time.