Defending champions England made an inauspicious start to the tournament in Switzerland when they lost to France, but they went on to secure their second major trophy against Spain, who had beaten them in the 2023 World Cup final.
"I just can't believe it. I have a medal around my neck and we have a trophy," Wiegman told BBC One.
"It has been the most chaotic tournament on the pitch -- all the challenges we had on the pitch against our opponent.
"From the first game it was chaos. Losing your first game and becoming European champions is incredible.
"Football is chaos."
England won the penalty shootout 3-1 after the match in Basel finished 1-1 following extra time.
"We said we can win by any means and that's what we have shown again today. I am so proud of the team and the staff. It is incredible," Wiegman said.