Page "Dijkstra's algorithm" Paragraph 14

Continue this process of updating the neighboring intersections with the shortest distances, then marking the current intersection as visited and moving onto the closest unvisited intersection until you have marked the destination as visited.

Once you have marked the destination as visited ( as is the case with any visited intersection ) you have determined the shortest path to it, from the starting point, and can trace your way back, following the arrows in reverse.