The teenager is currently filming his scenes and said it has been "perfect" so far.
“I’m really excited to be joining the cast of EastEnders – so far it’s been perfect," said Bobby, who also has a modelling career.
"Everybody has been so beautiful to me and made settling in easier than I could’ve hoped.
“Stepping into the acting world has always been a vision of mine and doing that with EastEnders as a Slater is a blessing, I’m very grateful. Loving every minute of Freddie so far and can’t wait to see what’s in store for him in Walford.”
Bobby was just five when Goody died in 2009 at the age of 27 after battling cervical cancer, and his brother was four.
Goody loved EastEnders and in 2006 it was reported that she asked the soap's stars Kara Tointon (Dawn Swan) and James Alexandrou (Martin Fowler) to put in a good word for her for a role after a chance meeting at V Festival.
Freddie Slater is set to arrive in Albert Square this summer.
He was last seen in Walford in May 2006 when he and his mother left to start a new life. He is now 18 and returning to Albert Square, where he is set to find himself on a path that could lead to heartbreak.
Show bosses said the character is "a bundle of energy and a truckload of trouble" and that although he has a heart of gold he "can’t help getting himself into mischief".
The soap's executive producer Chris Clenshaw said: “Freddie Slater is a chaotic 18-year-old with a sensitive soul.
“A modern-day lad who’s in touch with his spiritual side. He’s philosophical, accepting, but full of mischief and makes mistakes.
“Bobby is an amazing young addition to the EastEnders cast who brings heart and humility to the role of Freddie Slater and I can’t wait for audiences to get to know him.”
Additional reporting from PA.
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