Initially, the Roman calendar only had ten months of about 30 days each: March, April, May, June (each named for gods), and the rest were based on numbers (Sept-ember = 7th month, Oct=8, Nov=9, Dec=10). The winter was considered a period without months. http://en.wikipedia.org/wiki/Roman_calendar#Calendar_of_Romulus

Numa Pompilis divided the monthless winter into two new months, January (for Juno/Hera) and February (for februum, a purification tool and ceremonies regarding death at the end of the year). The Romans considered odd numbers lucky, so all months were renumbered to have either 29 or 31 days. February, the end of the year, was comprised of two odd-numbered periods. Intercalaris, a sort of leap-month, was inserted as needed to keep the months in line with the seasons. The length of a year alternated between 355 and 375 days depending on Intercalaris. http://en.wikipedia.org/wiki/Roman_calendar#Calendar_of_Numa

Julius Caesar reformed the calendar again to get rid of Intercalaris and match the months permanently to the seasons. This reform brought the regular year from 355 up to 365 days. The extra days were distributed across the months, leaving all months alternating with either 30 or 31 days. February, as the last month of the year, was given the remainder of 28, and on leap years (to account for the extra 1/4 day in the calendar) returned to the previously-held status of 29 days. http://en.wikipedia.org/wiki/Julian_calendar#Table_of_months

Later calendar changes renamed the month of Quintius to Julius (July) in Caesar's honor, Sextilius to Augustus after Augustus Caesar, placed the end of the year at the end of December, and moved days from the 30/31/30/31 pattern into months to honor their namesakes with longer months. February was never changed.

So, the short answer to your question is Julius Caesar in 45 B.C., in order to establish a full-year calendar permanently in sync with the seasons.