Wiktionary
phr. (context idiomatic English) There is nothing more to say or to do concerning the matter.
Wikipedia
"That's That" (explicitly titled "That's That Shit") is the second single by Snoop Dogg from the album Tha Blue Carpet Treatment. The song was the first single taken from the album in the United Kingdom, however the single only achieved notable success in the U.S., where it reached #20 on the Billboard Hot 100 chart. The song samples the melody played in the 1988 film Coming to America during the bathroom scene when Eddie Murphy gets washed by female servants.
"That's That" is a song written by Hugh Prestwood, and recorded by American country music artist Michael Johnson. It was released in August 1988 as the third single and title track from the album That's That. The song reached #9 on the Billboard Hot Country Singles & Tracks chart.
Usage examples of "that's that".
I don't propose to take a bath if I don't feel like it, and that's that.
Neufeld and his men will be up with us any minute here - and if they catch up on this cliff-face, well that's that.