South Africa Under-20s cap Thomson, whose father is Scottish, will provide cover for Finn Russell during his Six Nations participation with Scotland.
Thomson, 21, has played six times in Super Rugby for the Stormers.
Hughes, 23, returns to Glasgow's line-up for Friday's meeting with Scarlets after agreeing his new two-year deal.
And with New Zealander Dave Rennie replacing Warriors' Scotland-bound head coach Gregor Townsend next season, Hughes revealed extending his stay was an "easy decision".
"I'm looking forward to Dave Rennie coming in," Hughes said. "It'll be good to learn from him."
Hughes has played 24 times for the Warriors since 2014, scoring three tries in the process, and has two Scotland caps.
And Townsend added: "Rory is an important member of our squad and it's great that he's decided to continue his career at Scotstoun.
"He's played really well this season and there is a lot more to come from him in the future."
Of Thomson's arrival, Townsend said: "It's a bonus for us to be able to bring in someone of Brandon's quality and potential during a period when we have a number of players away on Test duty.
"He has fitted in really well so far and even training in the snow yesterday didn't seem to phase him."
Thomson added: "I was over in Zimbabwe playing a warm-up game for the Stormers when I got the call to say I could fly over here and it all happened pretty quickly.
"I came over with the main goal of getting some experience and it's good to play in a different environment and for a great club.
"I'm structured, physical and I like to run the ball out wide and keep the game loose."
Glasgow Warriors have signed fly-half Brandon Thomson on a two-month contract and have extended wing Rory Hughes' stay with the club until May 2019.