International air travel has already spread Ebola virus disease (EVD) to major cities as part of the unprecedented epidemic that started in Guinea in December 2013. An infected airline passenger arrived in Nigeria on July 20, 2014 and caused an outbreak in Lagos and then Port Harcourt. After a total of 20 reported cases, including 8 deaths, Nigeria was declared EVD free on October 20, 2014. We quantified the impact of early control measures in preventing further spread of EVD in Nigeria and calculated the risk that a single undetected case will cause a new outbreak. We fitted an EVD transmission model to data from the outbreak in Nigeria and estimated the basic reproduction number R0 = 9.0 (95% confidence interval [CI]: 5.2-15.6). We also found that the net reproduction number Rt fell below unity 15 days (95% CI: 11-21 days) after the arrival of the index case. Using the estimated value of R0 in Nigeria, we calculated that the risk of an outbreak from a single undetected case was 89% (95% CI: 81-94%). Even though R0 can be high, our study illustrates the time window for successful containment of EVD outbreaks caused by infected air travelers.