Scotland cap Swinson hasn’t played since November after breaking his hand during Scotland’s Autumn Test victory over Samoa on 11 November, while Cummings has also been sidelined with a hand injury.
Australian centre Sam Johnson also returns to the starting line-up after recovering from the broken jaw he sustained against Montpellier in December’s Champions Cup meeting.
Warriors head coach Dave Rennie welcomed the return of the three players, adding: “Sam, Scott and Tim are all influential players for us so to have them back is a huge boost.
“Although we were disappointed to only get a draw against the Dragons, we played the game in the right areas of the field and showed good attacking intent.
“The Cheetahs are a good side across the park and we know we’re going to have to be more clinical with our possession this Friday to get the result.”
Rob Harley will skipper the side as he equals Graeme Morrison’s record 177 appearances for Glasgow.
Glasgow have lost just once in 14 Pro14 fixtures, and defeated Cheetahs 29-26 in October in Bloemfontein.
Glasgow: Ruaridh Jackson, Lee Jones, Nick Grigg, Sam Johnson, Niko Matawalu, Adam Hastings, George Horne, Alex Allan, James Malcolm, Siua Halanukonuka, Tim Swinson, Scott Cummings, Rob Harley, Chris Fusaro, Matt Fagerson.
Replacements: Grant Stewart, Oli Kebble, D’Arcy Rae, Matt Smith, Adam Ashe, Henry Pyrgos, Brandon Thomson, Ratu Tagive.