Former England captain Cook, 34, who retired from international cricket this year, was his country's most-capped test player and record test run scorer.
Welsh cyclist Thomas, 32, has won three world championships and two Olympic gold medals along with this year's Tour de France, while the honours for Southgate and Kane follow England's World Cup run in Russia this Summer in which the team finished fourth, their best result since victory in 1966.
Two members of the team who rescued 12 junior footballers and their coach from a flooded cave in Thailand, Richard Stanton and John Volanthen, received the George Medal for gallantry.
A knighthood goes to writer Philip Pullman, whose books include the "His Dark Materials" trilogy, while "Gruffalo" children's author Julia Donaldson, 70, is awarded a CBE.
CBEs also go to Scottish violinist Nicola Benedetti, 31, and actress Sophie Okonedo, 50.
The New Year's honours have been awarded since Queen Victoria's reign in the 19th century and aim to recognise not just well-known figures but those who have contributed to national life through often selfless and unsung contributions over many years.
The biannual honours list is released on the Queen's official birthday in June and at the end of each year.