The 23-year-old Thomson has signed an 18-month contract, replacing former Kayserispor goalkeeper Deniz Dogan Mehmet, who has left the Bairns.
Thomson had joined Accies from Queen of the South in September but made only one appearance.
Bairns boss Peter Houston was delighted to sign the Falkirk-born player.
"Robbie is still a fairly young goalkeeper in terms of age but has had good experience playing in the Championship," said Houston, who released 24-year-old Mehmet after five appearances for Falkirk.
"I have been impressed with the lad anytime I have watched him."
German defender Sowah, 24, had joined Accies in the summer after leaving Hamburg and made seven appearances, his last being Saturday's 1-1 draw with Motherwell.
He exits New Douglas Park along with Trinidad and Tobago forward Richard Roy, the 29-year-old who also joined in the summer on a short-term contract after leaving Defence Force in his homeland but who made only two Accies appearances.
Meanwhile, Steven Boyd and Conor Scullion are back at Hamilton following loan spells.
Forward Boyd, 19, scored five goals in 16 appearances for Albion Rovers, while midfielder Scullion, 17, played 11 times for League One rivals Airdrieonians.
Goalkeeper Robbie Thomson has joined Falkirk after being released by Hamilton Accies along with forward Richard Roy and defender Lennard Sowah.