The first goods will begin to flow under an Africa-wide free-trade pact on Friday, the culmination of more than five years of negotiations on cutting cross-border tariffs.

The accord comes to fruition at a time when trade tensions are rising across much of the rest of the world. The 55-nation Africa Union (AU) will mark the occasion in a ceremony that comes just hours after the UK leaves the European Union’s single market and a new post-Brexit trade agreement enters into force...