Defender Shehu Abdullahi and Leon Balogun are the other two players who will sit out the biennial African football showpiece being hosted by Cameroon and which runs from January 9 to February 6.
Osimhen has been ruled out after he contracted coronavirus and has yet to fully recover from facial fractures that required surgery, while Watford will not release Dennis after they received his invitation for the tournament too late.
Osimhen and Dennis have been replaced by Henry Onyekuru of Olympiakos and Slavia Prague's Peter Olayinka respectively.
Nigeria accused Watford of "baring fangs" in their treatment of Dennis but Claudio Ranieri, the manager of the Premier League club, insisted talks between the team and the Super Eagles had been amicable.
"They have a lot of players, and they changed the manager then they change everything, and then we were ready," Ranieri said Friday.
"We knew we were ready to give the players, but they didn't do this. And then the two boards spoke and then for me it's OK."
The Italian added: "I am only the manager, only the coach, and I accept everything."
Nigeria confirmed their squad on Friday, adding in a statement: "In-form rapid raider Emmanuel Dennis, whose English club Watford is baring fangs, has been excused to provide room for Czech Republic-based forward Peter Olayinka."
Ranieri, however, was adamant Dennis had no qualms about thew situation, saying: "I knew they were speaking, the board and Nigeria board, and I accept every decision they find, and that, for me, is finished.
"I've spoken with him, of course he wanted to go, to play, but he also wanted to help Watford. I accept the decision of the board and the Nigeria team."
Venezia's Tyrone Ebuehi and Oluwasemilogo Ajayi -- who plays for second tier English side West Brom -- come in for Abdullahi and Balogun.
Goalkeepers: Francis Uzoho (AC Omonia/CYP), John Noble (Enyimba), Daniel Akpeyi (Kaizer Chiefs/RSA), Maduka Okoye (Sparta Rotterdam/NED)
Defenders: Chidozie Awaziem (Alanyaspor FC/TUR), Kenneth Omeruo (CD Leganes/SPA), Oluwasemilogo Ajayi (West Bromwich Albion/ENG), William Ekong (Watford/ENG), Olaoluwa Aina (Torino FC/ITA), Jamilu Collins (SC Padeborn 07/GER), Tyrone Ebuehi (Venezia FC/ITA), Zaidu Sanusi (FC Porto/POR), Olisa Ndah (Orlando Pirates/RSA)
Midfielders: Frank Onyeka (Brentford/ENG), Joseph Ayodele-Aribo (Rangers/SCO), Wilfred Ndidi (Leicester City/ENG), Chidera Ejuke (CSKA Moscow/RUS), Kelechi Nwakali (SD Huesca/SPA)
Forwards: Ahmed Musa (Fatih Karagumruk/TUR), Samuel Chukwueze (Villarreal FC/SPA), Henry Onyekuru (Olympiakos FC/GRE), Moses Simon (FC Nantes/FRA), Sadiq Umar (UD Almeria/SPA), Taiwo Awoniyi (Union Berlin/GER), Odion Jude Ighalo (Al-Shabab Riyadh/KSA), Alex Iwobi (Everton/ENG), Kelechi Iheanacho (Leicester City/ENG), Peter Olayinka (SK Slavia Prague/CZE)
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