He has also served as a Judge ad hoc in three cases before the International Court of Justice (ICJ) since 2014.
[2] He began his career as an attorney in private practice from 1961–1968 with the law firm of White & Case LLP.
Brower has served since 1983 as a judge of the Iran-United States Claims Tribunal in The Hague, The Netherlands, where he was a full-time member from 1984 to 1988.
[4] Since 2014, Brower has also been judge ad hoc of the International Court of Justice.
As of October 2023 he is a judge in two active cases by appointment of the United States:[5] He also was a judge ad hoc of the International Court of Justice in a case by appointment of Colombia until he resigned on 5 June 2022: Brower has served also as a judge ad hoc of other international judicial panels, such as the Inter-American Court of Human Rights; as a member of the Register of Experts of the United Nations Compensation Commission in Geneva (UNCC); and as a member of the Panel of Arbitrators of the International Centre for Settlement of Investment Disputes (ICSID).