The 19-year-old plays Freddie Slater, son of Maureen “Little Mo” Slater, and is currently filming scenes set to air this summer.
The character Freddie was last seen in Walford in May 2006, when he and his mother left to start a new life.
Now he returns to Albert Square at the age of 18 and finds himself on a path that can lead to heartbreak.
Big Brother star Goody, who died in 2009 at age 27 after being diagnosed with cervical cancer, had Bobby and his brother Freddy, now 17, with fellow reality TV star Jeff Brazier.
An avid fan of EastEnders, she reportedly petitioned two of her stars in 2006 to talk to their bosses about getting her a part during a chance meeting at V Festival.
Bobby Brazier said: “I’m really excited to join the EastEnders cast – so far it’s been perfect. Everyone has been so lovely to me and made it easier for me to settle down than I could have hoped.
“Entering the acting world has always been a vision of mine and to do that with EastEnders as Slater is a blessing, I am very grateful.
“Love every minute of Freddie so far and can’t wait to see what’s in store for him in Walford.”
Describing his character, the show bosses said, “A bundle of energy and a truckload of trouble, Freddie Slater has a heart of gold but can’t help but get himself into mischief.
“While he’s sweet like his mom, he’s certainly not shy and knows how to cause a stir everywhere – but is he a true Slater at heart?”
EastEnders executive producer Chris Clenshaw said: “Freddie Slater is a chaotic 18-year-old with a sensitive soul.
“A modern boy in touch with his spiritual side. He is philosophical, accepting, but full of mischief and mistakes.
“Bobby is a great young addition to the EastEnders cast who brings heart and humility to the role of Freddie Slater and I can’t wait for the audience to get to know him.”