The singer was voted through by the public after an emotional performance of Vera Lynn's famous We'll Meet Again in memory of his late wife Joan.
Black and white images of the pair flashed behind Thackery inside the Hammersmith Apollo in London.
The audience waved their arms back and forth and poppies rained from the ceiling as Thackery sung backed by a troupe of Chelsea Pensioners.
After he was announced as winner, co-host Ant McPartlin asked if he knew what had just happened.
He said: "Sorry what. I have vague idea, yes. Thank you very much. Thank you."
"It's just starting to sink in," he later added.
Stand-up comedian Kojo Anim also made it through to the final after securing all four judges' votes.
Fellow comic John Archer also made the top three, but the judges' unanimous decision sealed his fate and he was sent home.
"That's alright. I had a golf match organised for Sunday anyway," he quipped to the crowd after.
Thackery and Anim join Flakefleet Primary School, Dave & Finn, magic group 4MG and Siobhan Phillips in the final.
Dance troupe KNE, singer Rob King, Angels Inc, Gomonov Knife Show and boyband Chapter 13 were all sent home following the public vote.
The third live-semi-final also saw a live performance from The X Factor winner James Arthur.