They are both correct in different contexts.
'There is/there are' is used to introduce someone/something (to talk about it for the first time).
There is a new restaurant in my neighborhood.
"the" is used to talk about a SPECIFIC person or thing.
The French restaurant on West Place is quite delicious, but expensive.
In your example, here are the contexts where I would use one or the other:
Mary and Tom are sitting in their living room. The doorbell rings and their son goes to answer. He comes back and says, "There's a boy here who wants to talk to you."
Mary is the principal of a primary school. She gets a phone call from the local hospital saying that Mrs Henley has been brought into the hospital. Mrs. Henley will need to stay in the hospital and will not be able to pick up her son Timmy. The Henley's neighbor will pick him up and bring him to the hospital to see his mother. Mary needs to tell Timmy. She sends her assistant out to fetch him and bring him to the office. The assistant goes to Timmy's classroom, picks him up and brings him to the office. Then she peeks her head into Mary's office and says, "The boy is here."