It is easy to see why this would be hard for you to find as it is not clearly stated -- Joe doesn't quite come out and say it.
But you should look at the part toward the end of Chapter 27 where Joe talks about his visit to Miss Havisham. Miss Havisham tells Joe that Estella is back home and she (Estella) would be happy to see Pip. She wants Joe to tell Pip this.
When Joe tells Biddy about this, Biddy tells him he should go tell Pip in person. She says Pip would like that.
So Joe comes to London to tell Pip what Miss Havisham said. But I think Joe also comes to see Pip because he misses Pip, who has never come back to see them.