A silane crosslinkable silicone rubber composition including: with respect to 100 parts by mass of a base rubber containing a millable silicone rubber, 1 to 15 parts by mass of a silane coupling agent graft-bonded to the base rubber; 0.5 to 300 parts by mass of an inorganic filler; and 0.01 to 0.5 parts by mass of a silanol condensation catalyst, a method of producing the same, a silane crosslinked silicone rubber formed body obtained by using the silane crosslinkable silicone rubber composition, and a method of producing the same, and a silane crosslinked silicone rubber formed article including the silane crosslinked silicone rubber formed body.