Your could use the CONCAT function to build the date
UPDATE table SET newdate = CONCAT(year,'-', month,'-', day)
Unfortunately I couldn't get mysql to accept an alpha month (don't know what server u use) but as a workaround yo could
UPDATE table SET newdate = CONCAT(year,'-01-', day) WHERE month='January'
UPDATE table SET newdate = CONCAT(year,'-02-', day) WHERE month='February'
etc.
hth