In 1990 he moved to London, where he was a managing director with responsibility for the firm's banking department and corporate finance activities in Europe.

[10] Bradway oversaw the acquisition of Iceland-based DeCODE Genetics in 2012,[11] Onyx Pharmaceuticals in 2013,[12] and a 20.5% equity stake in Beijing-based BeiGene in 2020.

[18] In June 2017, he gave the keynote address at the commencement ceremony for graduates of the University of California, Los Angeles Anderson School of Management.

[20][21] Following the 2020 murder of George Floyd in May 2020, Bradway issued a statement condemning the murder as "senseless" and pledging to address racial inequality at Amgen, stating, "Let's take inspiration from science and trust that progress, like knowledge, builds upon itself, incrementally improving on what exists today until the cumulative adds up to something profound.

"[22] On October 1, 2020, Bradway testified before the House Oversight Committee and was questioned by Rep. Katie Porter (D. Cal) for his considerable compensation.