Ogunjobi had previously ruled out a home game before the World Cup finals.
"It has been difficult to get a team to agree to come to Lagos.
"We had to spread our tentacles to secure this opponent," Ogunjobi told BBC Sport Online.
Nigeria are drawn with England, Argentina and Sweden in group D at the World Cup finals in Korea/Japan.
Nigeria beat Kenya in Lagos four years ago to qualify for the 1998 World Cup.
Ogunjobi added that another warm-up match, against Jamaica in London, has been confirmed for 18 May .
"If you add the China and Republic of Ireland friendlies on May 11 and May 16, it means we have four major tests for our boys before the World Cup."
Ogunjobi could not say whether coach Adegboye Onigbinde will recall some of the established players, including defender Taribo West and goalkeeper Ike Shorounmu, for the warm-up against Kenya.
The NFA said the team will be subsequently pruned down to 30 players, who will begin Nigeria's final preparations for the World Cup on 8 May.
Ogunjobi said the Super Eagles will depart for Japan on 19 May.
Goalkeepers: Vincent Enyeama (Enyimba), Etta Ijoh (Egypt-based),
Austin Ejide (Gabros/Ngr), Ademola Bankole (Crewe/Eng).
Defenders: Joseph Yobo (Marseille/Fra), Daniel Shittu (Queens
Park Rangers/Eng), Isaac Okoronkwo (Shakhtar Donetsk/Ukr),
Christopher Justice (Antwerp/Bel), Rabiu Afolabi (Standard
Liege/Bel), Eric Ejiofor (Maccabi Haifa/Isr), Obinna Nwaneri, Seyi
Olajenbesi (Julius Berger/Ngr), Christopher Kanu (Ajax/Ned), Efe
Midfielders: Austin 'Jay Jay' Okocha (Paris Saint Germain/Fra), Osaze Odemwegie (Insurance), Ekpe Ekong (Reggiana/Ita), Ndubuisi Eze (Julius Berger), Karibe Ojigwe (Bayer Leverkusen/Ger), Wilson Oruma (Servette Geneva/Swi), Pius Ikedia (Ajax/Ned).
Forwards: Benedict Akwuegbu (Shenyeng Gendi/Chn), Julius Aghahowa (Shakhtar Donetsk/Ukr), Ade Akinbiyi (Crystal Palace/Eng), Emeka Ugali (Monza/Ita), Samuel Ayorinde (Switzerland-based), Bartholomew Ogbeche (Paris Saint Germain/Fra), Rabiu Baita (Kano Pillars), John Utaka (Al Saad/Qat), Femi Opabunmi (Grasshopper Zurich/Swi).