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Arsenal conceded two late goals to lose 2-1 at Brighton and Hove Albion, their second defeat since the restart of the Premier League.
A late goal from Nketiah gave Arsenal a 2-1 home win over West Ham United after Michail Antonio's first-half strike for the visitors had cancelled out Alexandre Lacazette's 50th goal for the Gunners.
The 2-1 victory over Chelsea earned Arsenal a record-extending 14th crown in the competition - and a spot in next season's Europa League.
The Premier League announced an emergency meeting on Friday.
The 37-year-old has never managed a club before but Arsenal's head of football Raul Sanllehi felt the former captain was the "perfect person" among several top-class candidates.
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