Councillors on the development control committee voted to allow the development, which will see the creation of 12 permanent jobs in the eatery which will open from 8am to 11pm from Monday-Saturday.
They welcomed the development of the shelter, which had been unused for a number of years and fell into disrepair after years of use by drunks and homeless people.
Councillor Judith McMahon said: "I would like to commend this particular conversion, it is the most empathetic use of the building and is absolutely superb.
"We should be very pleased and it will add a lot to Southend, both with its design and it being in-keeping with the local area."
The front of the venue will include open-air seating, with the possibility of music - such as violin performances - while people eat.
Antonia Waite, daughter of former council leader Anna Waite, was awarded the lease for the cafe – provisionally called Seaside Rock – and now planning has been approved she hopes to start building in late summer.