The 22-year-old Zambia striker will join the Foxes on a five-year deal, subject to Premier League and international clearance.
Brendan Rodgers' men were wobbling after losing their previous two top-flight matches but produced a dazzling attacking display against the insipid visitors at the King Power Stadium.
Premier League: Manchester City beat Tottenham to extend lead to seven points; Liverpool stunned by Leicester
Pep Guardiola's side stretched their English top-flight record run to 16 successive victories in all competitions.
Premier League: League-leaders Manchester City thrash Liverpool; Harry Kane inspires Tottenham to win
Inspired by Gundogan's goals and Phil Foden's stylish display, City moved 10 points clear of fourth-placed Liverpool after their first win at Anfield since 2003.
Premier League: Brendan Rodgers hopeful of Leicester City managing well without talisman Jamie Vardy
Vardy has had an operation on a long-standing hernia problem and last week Rodgers said he would be sidelined for "a few weeks".
Rodgers had spoken earlier in the week of getting the best out of Vardy in the time he has remaining at the top as he has also been hindered by a recurring hip problem.
Premier League: Leicester City need to begin planning for life without Jamie Vardy, says Brendan Rodgers
Vardy has been pivotal to the Foxes' impressive Premier League campaign thus far, scoring 13 times in 19 games.
Premier League: Chelsea fail to ease pressure on Frank Lampard after draw against Villa; Leicester and Palace share spoils
Chelsea failed to ease the mounting pressure on manager Frank Lampard as Aston Villa came from behind to earn a 1-1 draw at Stamford Bridge on Monday, as a coronavirus outbreak at Manchester City caused their clash at Everton to be postponed.
A first league victory in nearly two months was vital, therefore, to boost Arsenal players' fragile confidence — even if it only lifted them into 14th place.
Premier League: Manchester United decimate old rival Leeds 6-2; Leicester City dent Tottenham's title challenge
United, who made a stuttering start to the season, now have 26 points — five behind leaders Liverpool with a game in hand.
Premier League: Son Heung-min, Harry Kane score as Tottenham win North London derby; Liverpool beat Wolves
Jose Mourinho's men beat faltering Arsenal 2-0 in front of 2,000 vocal fans at Tottenham Hotspur Stadium to leapfrog Chelsea.
In a written statement to the High Court, Vardy said she was pregnant at the time and feared she could lose her unborn baby due to the stress of Rooney's allegations.
Premier League: Kevin de Bruyne misses penalty as Manchester City, Liverpool share spoils; Kane nets 150th goal in Spurs' win
Kane headed in a late winner in a 1-0 victory against struggling West Brom to lift Jose Mourinho's side above Southampton after their fourth win in five league games.
Premier League: Brendan Rodgers jokes he 'got lucky' after Leicester City beat Marcelo Bielsa's Leeds United
Brendan Rodgers' Leicester have made their joint best-ever start to a top-flight campaign, even better than when they won the title in the 2015/16 campaign.
Benfica and Rangers earned their second straight victories while Hoffenheim and Wolfsberg cruised to big away wins.
Premier League: Jamie Vardy seals victory for Leicester against Arsenal; Wolves, Newcastle share points
Arsenal are languishing in 10th after a second consecutive league loss following their 1-0 defeat at Manchester City last weekend.
For the first time ever, Guardiola saw one of his teams concede five goals in his 686th game as a manager with City, Bayern Munich and Barcelona.
Premier League: Dominic Calvert-Lewin nets, James Rodriguez shines as Everton beat Tottenham; Leicester victorious
It was the first time Tottenham coach Jose Mourinho — who has previously managed Chelsea and Manchester United — has lost his opening match of a Premier League season, having been unable to sign a backup option to Kane.
Premier League: Jamie Vardy signs one-year extension with Leicester City after Golden Boot-winning season
The Foxes have rewarded Jamie Vardy after he scored 23 goals to claim the Premier League's Golden Boot last season.
Striker Jamie Vardy won the Golden Boot award after finishing the season with 23 goals but no other Leicester player reached double figures.