The rapper will hand over $450,000 (£332,000) to end the two-year spat linked to Chapman's claim Minaj used portions of "Baby Can I Hold You Tonight" in her song "Sorry".
Although the song Minaj wrote with Nas was never released, a leaked version went viral.
Chapman accused Minaj of sharing the song with DJ Funkmaster Flex, who played it on his radio show.
The track featured a sample of the dancehall track "Sorry" by Jamaican artist Shelly Thunder, which was based on "Baby Can I Hold You Tonight". Chapman refused Minaj's permission to use her song.
In an earlier judgement it was ruled Minaj's sample constituted "fair use," but allowed Chapman's complaint to go to trial.
The proceedings will now not be necessary after Chapman accepted Minaj's settlement offer, which reportedly covers the "Fast Car" singer's costs and legal fees.
"I am glad to have this matter resolved and grateful for this legal outcome which affirms that artists' rights are protected by law and should be respected by other artists. I was asked in this situation numerous times for permission to use my song; in each instance, politely and in a timely manner, I unequivocally said no. Apparently Ms. Minaj chose not to hear and used my composition despite my clear and express intentions," Chapman said in a statement obtained by PEOPLE.
"As a songwriter and an independent publisher, I have been known to be protective of my work. I have never authorized the use of my songs for samples or requested a sample. This lawsuit was a last resort — pursued in an effort to defend myself and my work and to seek protection for the creative enterprise and expression of songwriters and independent publishers like myself."