Emery was relieved of his duties on Friday morning following a run of seven games without a win.
Spaniard Emery succeeded Arsene Wenger in May 2018 and took Arsenal to the Europa League final previous year but frustration with the club's erratic league form this season has grown, with the side sitting eighth in the table with 18 points from 13 games.
He was replaced by Freddie Ljungberg, who takes charge on a part-time basis, after head of football Raul Sanllehi and managing director Vinai Venkatesham had travelled to the United States to talk to Kroenke and his father, Arsenal owner Stan Kroenke.
It might not come as a surprise that Unai Emery was the latest of these to lose his job. But he failed to live up to the expectations of Arsenal and the Premier League, and the frustration had been building amongst supporters.
The decision has been taken due to results and performances not being at the level required.We have asked Freddie Ljungberg to take responsibility for the first team as interim head coach. Emery previously coached at Lorca Deportiva, Almeria, Valencia, Spartak Moscow, Sevilla and Paris Saint-Germain, before landing at Arsenal.
However, that consistency disappeared in the final games of the season, as Arsenal finished fifth in the league and lost to Chelsea in an all-English final of the Europa League.
The Arsenal Supporters' Trust released a statement saying Emery's dismissal was "unfortunate but inevitable".
The next Arsenal manager will be ...?
The 48-year-old Spaniard was sacked following the 2-1 home defeat to Eintracht Frankfurt in Thursday's Europa League match.
And so the search for a new head coach at the Emirates Stadium is underway, and a range of candidates are rumoured to be in line.
The Swede, who was a crucial part of Arsenal's success in the early 2000s under Arsene Wenger, is very much a modern manager, who puts serious emphasis on wide players, as well as dynamic midfielders.
"For the moment it's for the future of the football club", he told Arsenal's website.
Joining Allegri and Leicester manager Rodgers on the list are Manchester City assistant manager Mikel Arteta, Napoli boss Carlo Ancelotti and Wolves manager Nuno Espirito Santo.
Arsenal's league form has fallen away badly with five Premier League matches without a win - they are the only side in the top half of the table with a negative goal difference. Two of the men who made the decision to appoint Emery - chief executive Ivan Gazidis and head of recruitment Sven Mislintat - departed within nine months, leaving the Spaniard more exposed to change.