Most internet sites indicate that he arrived on the ship Safety in 1635.
Below is the text noting this ship's passenger list which can be read online.
The original lists of persons of quality; emigrants; religious exiles; political rebels; serving men sold for a term of years; apprentices; children stolen; maidens pressed; and others who went from Great Britain to the American Plantations, 1600-1700 : with their ages and the names of the ships in which they embarked, and other interesting particulars; from mss. preserved in the State Paper Department of Her Majesty's Public Record Office, England (1874)
Author: Hotten, John Camden, 1832-1873
The ship Safety sailed from the port of London to America, August 10, 1635.
John Graunt was the master of the ship. Pages 121-123.
