The 24-year-old forward joins the Maryhill side following his release from Huddersfield Town.
The former Falkirk player will go into Alan Archibald's side for the trip to Ross County on Saturday.
The Jags boss said: "I am very content with the shape of the squad and this signing complements it nicely.
"I am perhaps a little shy in numbers in that area and as I have said many times I will be needing every member of the squad throughout the course of the season.
"Another good thing that Kallum offers is versatility as he can play up front as well as in a wider role where I think he is a top performer.
"Subject to all the paperwork being completed he will be in the squad for Saturday."
Archibald believes his Thistle side will come across the "template for success" in the Scottish Premiership when they travel to Dingwall.
The Staggies were arguably the surprise package of last season after being promoted from the First Division for the first time.
Widely tipped to struggle, Derek Adams' side secured a top-six finish on the back of an impressive home record which saw them lose only three league games in front of their own fans.
The Maryhill Magyars started life in the Premiership with an encouraging goalless draw against Dundee United at Firhill last Friday before beating Ayr United 2-1 at home in the League Cup on Tuesday night.
Preparing for the trip to the Highlands, Archibald said: "It will probably be a harder game than the game against Dundee United.
"We know how good and how well-organised Ross County are.
"They are our template to success probably.
"They have a great home record and that is something we hope to have and if we do that, then we won't be far away.
"So we have a nice hike up the Highlands but we are used to it.
"We were up at Ross County a couple of years ago, the only difference this time is we are getting a hotel overnight.
"We didn't used to get that - it used to be the eight o'clock bus.
"Our build-up will still be the same for this game and we will still be up for it.
"We just know these will be the harder games to try to get the boys up for, there won't be as big a crowd and things like that but we will be ready."
The former Thistle defender was encouraged by the way his team played against United, despite failing to take all three points.
He said: "It was good in a way to get last week over with, given the hype around the game.
"It was a great spectacle for the new league.
"None of the players had played an SPL game before and it was a bit of circus before the game with the media but they handled it well."