This was just announced by the Polo Museale Fiorentino (the Uffizi will be closed on New Year's day as usual).
Since Christmas Eve will be on Monday when the museums are usually closed the Uffizi and Accademia will be open from 8:15 AM to 6 PM. They will join the other museums, salons and villas normally open on the fourth Monday of each month: the Silver Museum and the Costume Gallery in the Pitti Palace, the Boboli Gardens, the Medici Chapels, Palazzo Davanzati, Orsanmichele, Ghirlandaio's Last Supper and the Medici villas at Petraia, Castello, Poggio a Caiano and Cerreto Guidi.
On New Year's Eve, December 31, which also falls on a Monday this year, the Uffizi Gallery and the Accademia Gallery will be open exceptionally from from 8:15 AM to 6 PM. To these are added the Bargello Museum, The museum of San Marco, Orsanmichele (which is only open on Mondays), the Convent of Santa Apollonia, and the Medici villas at Petraia, Castello, Poggio a Caiano and Cerreto Guidi.