Teenage striker Akpom has broken into the first team at the Emirates Stadium this season, making five appearances in all competitions.
Coquelin, meanwhile, was recalled from a loan spell at Championship side Charlton Athletic in November and has subsequently impressed in a holding midfield role.
Wenger - who added Gabriel Paulista and Krystian Bielik to his squad in the January transfer window - is delighted to have secured the services of Akpom and Coquelin for a longer period.
"I'm very happy with the business we did [in January], Wenger said on Friday.
"We met our targets and extended Akpom and Coquelin's contracts"
Arsenal visit local rivals Tottenham on Saturday for a north London derby that promises to be a crucial game in the race for UEFA Champions League qualification.
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