The former Southampton boss has departed The Valley after arriving in the position in March - the day before Danny Cowey arrived at Pompey.
Adkins leaves the Addicks post with his side in the League One relegation places, six points behind the Blues after 13 games.
The home defeat to Accrington proved the final straw, with the 3-2 defea making it one league win in eight for Charlton.
Charlton owner Thomas Sandgaard told the club’s official site: ‘Nigel joined us at the end of last season and had an immediate impact, as we finished the season well, just missing out on a play-off place on goal difference.
‘Unfortunately, we haven’t been able to carry that form into this season.
‘I’d like to thank Nigel for his hard work, positivity and continued professionalism during his time at the club.
‘We are all disappointed that it hasn’t worked out this season and we wish him the very best for the future.’
Johnnie Jackson will take on the caretaker manager position supported by Jason Euell, as Charlton go to Sunderland this weekend.
Charlton have an FA Cup clash meeting with Hawks at the start of next month.
Paul Doswell’s men set themselves up for a trip to The Valley with an excellent 3-1 replay win over Torquay United last night at Westleigh Park.
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