Meanwhile, Motherwell, who won their previous visit to Rugby Park last season, could move five points clear of the bottom two with a victory.
Wright, who left St Johnstone in May after seven years in charge, said that it was an "easy decision" to take the job at Rugby Park and believes that it is the "perfect time" for him to return to management.
The 57-year-old will have little time to prepare for his first game in charge against a Motherwell side who Kilmarnock have already beaten this campaign, winning 2-0 away from home in December.
Last weekend's 2-0 defeat to St Mirren was their fifth successive loss in the league and Wright hopes to make an immediate impact and end this poor run of form with a victory on Wednesday, that could move Killie above Motherwell into ninth, four points clear of the bottom two.
Motherwell were unable to secure their third league win in a row as they lost 2-1 away to Celtic last weekend.
The Hoops survived a late scare from the Steelmen who, after pulling one back through midfielder Allan Campbell in the 66th minute, came close to finding an equaliser when Harry Smith's header was cleared off the line in added time.
That result was Motherwell's 11th defeat of the season and sees Graham Alexander's men remain in ninth place, just two points above the bottom two.
Prior to their defeat against Kilmarnock earlier this campaign, the Steelmen won both of their encounters with Killie last season, including a 1-0 away win in December 2019.
With an important match against basement club Hamilton coming up this weekend, a victory on Wednesday night would provide a massive boost for Alexander's side in their quest to avoid the drop.
Kilmarnock Scottish Premiership form: WLLLLL
Motherwell Scottish Premiership form: DDLWLL
Kilmarnock will be without key defensive duo Kirk Broadfoot (knee) and Stuart Findlay (ankle) who are both suffering with injuries, while left-back Calum Waters also remains out with a groin strain picked up in December.
Motherwell centre-back Declan Gallagher as well as left-backs Liam Grimshaw (illness) and Nathan McGinley (head) are all unavailable for selection, while goalkeepers Scott Fox and Trevor Carson continue to recover from their long-term injuries.
Kilmarnock possible starting lineup:
Rogers; Millen, Dicker, Medley, Haunstrup; Power, Mulumbu, Tshibola; Burke, Kabamba, McKenzie
Motherwell possible starting lineup:
Kelly; O'Donnell, Mugabi, Lamie, Carroll; Campbell, Crawford, Maguire; Long, Cole, Watt
We say: Kilmarnock 1-1 Motherwell
Both sides are hovering precariously above the relegation zone and know that a few more defeats could see them slip into the bottom two. With little to separate the two sides, we could see a draw played out on Wednesday evening.