They said they had been planning to attack the US and British embassy in the city of Abuja.
Since 2009 Boko Haram have been carrying out an armed rebellion against the Nigerian government.
They have allied themselves with Islamic State (ISIS) who have supplied weapons and fighters to the group.
They said: “The group had perfected plans to attack the UK and American Embassies and other western interests in Abuja.”
The security service said another suspected Boko Haram member, arrested on March 22, in northeastern Yobe state, confessed details of the plot.
Attacks have also taken place in neighbouring Cameroon and Niger.
In 2014 the group kidnapped hundreds of young female students from a college in Chibok.
The kidnappoing of the ‘Chibok Girls’ gained international attention. Despite a huge rescue operation and a #BringBackOurGirls awareness campaign, 195 of the 276 girls are still missing.
Earlier this year the Nigerian military announced they were beginning a “final offensive” against the militants.