Sincerely sorry to have to tell you, your button has what button-collectors call a "self-shank" back (the button's back itself forms the tunnel for thread to attach the button to cloth). The self-shank back means your button is a civilian "Fashion" imitation of the actual 1852-1941 US Navy button. Usage on civilian clothing is permitted because the imitation's emblem hasn't been in use by the Navy since 1941.
Additional evidence toward the Civilian Imitation identification is that your button lacks the very crisp, sharp detail seen on actual US Navy buttons... clearly visible in this photo of one, below. For example, notice that every feather in the eagle's wings is sharply detailed.
Update:
I found a photo showing your button's EXACT front, at the Waterbury Button Company's website, in the (civilian) "Fashion" category. Notice the eagle's round-ish very "puffy" chest and round-ish very "puffy" legs.