WAR DEPARTMENT, WASHINGTON, Dec. 25 -- 8 P.M.

To Maj.-Gen, Dix, New-York:

A dispatch has been received this evening by the President from Gen. SHERMAN. It is dated at Savannah, on Thursday, the 22d inst., and announces his occupation of the city of Savannah and the capture of one hundred and fifty guns, plenty of ammunition, and about 25,000 bales of cotton. No other particulars are given.

An official dispatch from Gen. FOSTER to Gen. GRANT, dated on the 22d instant, at 7 P.M., states that the city of Savannah was occupied by Gen. SHERMAN on the morning of the 21st, and that on the preceding afternoon and night, HARDEE escaped with the main body of his infantry and light, artillery, blowing up the iron-clads and the Navy-yard. He enumerates as captured 800 prisoners, 150 guns, 13 locomotives, in good order, 190 cars, a large lot of ammunition and materials of war, three steamers and 33,000 bales of cotton. No mention is made of the present position of HARDEE's force, which had been estimated at about 15,000.

The dispatches of Gen. SHERMAN and Gen. FOSTER are as follows:

SAVANNAH, Ga., Dec. 22.

To His Excellency, President Lincoln:

I beg to present you as a Christmas gift, the city of Savannah, with one hundred and fifty heavy guns and plenty of ammunition, and also about twenty-five thousand bales of cotton.

(Signed,) W.T. SHERMAN, Major-General.

STEAMER GOLDEN GATE, SAVANNAH RIVER, 7 P.M., Thursday, Dec.23.