Samoan international, Fa'atau, who signed for the Warriors during the summer from Wellington Hurricanes, brings with him a reputation of being one of the most exciting wingers in world rugby.
Fa'atau reached the final of last seasons Super XIV with the Hurricanes and became the tournaments top try scorer in the process.
Looking ahead to making his first appearance at The Arena, Fa'atau said: "I'm really looking forward to playing in front of the Glasgow fans for the first time.
"The weather has been pretty cold back home so it hasn't come as a shock to me yet and settling into the squad has been easy as well. Justin [Va'a] and OP [Opeta Palepoi] have been a great help."
On Magners League rugby at Firhill, Fa'atau added: "I suppose due to the weather, most people think that Magners League rugby won't be as expansive and as fast as the Super XIV, but playing at a football ground will hopefully mean that we can play at real pace throughout the entire season."
Fellow debutant, Brown, added: "The World Cup was an awesome experience so hopefully I will get the chance to play in some more in the future, however my focus has now fully turned to Glasgow.
"I'm settling in nicely and training is going well. All the boys have made me feel very welcome. I'm looking forward to tomorrow night and starting my Glasgow career on a high."
Glasgow head coach Sean Lineen concluded: "We're getting closer to our full strength side.
"We are developing some real competition for places, which is exactly what you need to drive a team forward.
"We are also getting closer to our European campaign, so I am looking for our boys to really front-up against a powerful Munster side."
Glasgow Warriors: Bernardo Stortoni; Lome Fa'atau, Andrew Henderson, Daryl Gibson, Thom Evans; Dan Parks, Chris O'Young; Ed Kalman, Fergus Thomson, Moray Low; Andy Newman, Alastair Kellock capt; Stevie Swindall, John Barclay, Kelly Brown Replacements: Eric Milligan, Michael Collins, Dan Turner, Johnnie Beattie, Sam Pinder, Scott Barrow, Hefin O'Hare