Namibian lock Koll joins his fellow countryman Tinus Du Plessis in the pack following his arrival in recent weeks, while Robinson, who joined Wasps this week from Leicester, gets a start on the wing.
In other team news, powerful young number 8 Billy Vunipola returns to Wasps colours for only his second appearance of the campaign having recovered from an infection which has kept him out for most of the season, while youngster and lifelong Wasps fan Will Robinson will hope to make his first ever appearance at Adams Park having been named on the bench.
Nineteen-year-old Robinson earlier this season became the first player at the club to play at senior level following graduation from the Wasps Academy Apprenticeship programme.
On the bench, London Welsh duo Mike Powell and Ashley Smith step up a league for the weekend while scrum-half Charlie Davies captains the side.
Meanwhile, Exeter coach Rob Baxter will welcome back James Hanks and Peter Short for the clash with Wasps.
The two second-row forwards have had to watch on as the Chiefs have made progress in both the Aviva Premiership and the Amlin Challenge Cup in recent weeks.
However, both men return to the starting XV for Exeter's latest cup assignment.
Short, a summer signing from Bath, has not featured for the Devon club since breaking his leg against Wasps back in September, while Hanks has been ruled out of action since coming off in the home game against Worcester Warriors in December.
For Baxter, though, having both players back amongst the first team picture is vital, especially as the season begins to crank up another notch.
The inclusion of the duo, along with that of a number of those who have been on the first team periphery in recent weeks, means Baxter has plenty of new options to choose from ahead of this weekend's tussle.
"We're looking forward to it," he said.
"We are going well in the Premiership; we've had a good weekend in Europe and this weekend gives us an opportunity to take a look at a few guys coming back from injury, whilst at the same time take a good, fresh, strong squad to Wasps.
"It's the kind of game, we feel, where we can put in a big performance from a few guys coming back and at the same time start to build some squad strength going into the Leicester game in a few weeks time.
"It's a big boost for us to have both Shorty and Hanksy back and if they come through strongly, we are starting to get near enough a fully-fit front five which is important to us.
"Recently we have had opportunities to rotate the front row, which again is important, and it helps keep everyone fresh.
"At the moment we're not quite sure what Craig Mitchell's involvement with Wales will be, so having everyone up and running going into those Premiership games will be vital.
"At the same time, it also keeps a happy camp because the more rugby you can get everyone playing, the happier people will be," added Baxter.
The Chiefs will also hand a first-ever start to Academy product Sam Hill.
On the bench, other up-and-coming youngsters, Jack Arnott and Sam Jones, are included for the first time, whilst England Under-20s prop Luke Cowan-Dickie will be hoping for more first team exposure off the bench.
Wasps: 15 Jack Wallace, 14 Lee Robinson, 13 Alex Cheesman, 12 Chris Mayor, 11 Charlie Ingall, 10 Ryan Davis, 9 Charlie Davies (c), 8 Billy Vunipola, 7 James Harris, 6 Tinus Du Plessis, 5 Ed O'Donoghue, 4 Heinz Koll, 3 Jeremy Castex, 2 Tom Lindsay, 1 Zak Taulafo.Replacements: 16 Nathan Morris, 17 Bob Baker, 18 Simon McIntyre, 19 Mike Powell, 20 Joe Burton, 21 Jonah Holmes, 22 Will Robinson, 23 Ashley Smith.
Exeter: 15 Myles Dorrian, 14 Bryan Rennie, 13 Phil Dollman, 12 Sam Hill, 11 Mark Foster, 10 Gareth Steenson (c), 9 Pat Phibbs, 8 James Phillips, 7 Ben White, 6 Dave Ewers, 5 James Hanks, 4 Peter Short, 3 Craig Mitchell, 2 Chris Whitehead, 1 Hoani Tui.Replacements: 16 Simon Alcott, 17 Luke Cowan-Dickie, 18 Chris Budgen, 19 Chris Bentley, 20 Aly Muldowney, 21 Junior Poluleuligaga, 22 Jack Arnott, 23 Sam Jones.
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