Nadim Gulamhuseinwala, 32, was attacked in the early hours of 25 July last year as he walked home through Green Park.
Thomas Connor and William Paton, both 20 and of Orpington, Kent, were found guilty at the Old Bailey of murder and robbery last week.
Connor, who had appeared on the dessert packets when he was 11, was given a minimum sentence of 25 years. He hit the doctor on the head with an iron pole and stamped on his face.
Paton, who searched through the doctor's pockets and stole money, was given a minimum term of 23 years' custody.