He finished the course in 3:28.209 and was followed over the line in a semi-final race by Eirik Veras Larsen of Norway and Rene Poulsen of Denmark.
Defending Olympic champion Tim Brabants came fourth and just made it into the A final with them.
After having to settle for silver four years ago despite being favourite, world champion Van Koeverden denied the thought of coming second again was playing on his mind.
He said: 'I am world champion in 1000m and we only race a big race once in a year, whether it's the world championships or the Olympics.
'I had a great 1000m when I was 22 at the (Athens 2004) Olympics. I had one bad one. I have put it behind me and I will race well on Wednesday.'
In the other semi-final race, German Max Hoff came first in 3:29.294 and was followed by Aleh Yurenia of Belarus and Anders Gustafsson of Sweden.
The A final line-up is completed by Francisco Cubelos Sanchez of Spain, who came fourth in the second semi-final in a time of 3:31.833.
In the individual C1 1000m, Sebastian Brendel won the first semi-final, while Frenchman Mathieu Goubel won the second.
Both will meet Hungary's 29-year-old paddler Attila Vajda, who also qualified for the final.
Speaking afterwards, Goubel, who finished seventh at Beijing 2008, said he was keen prove a point.
He said: 'Today my objective was to qualify for the final and I wanted to show my adversaries that I'm present.
'I wanted to make a mark for the final, so my job is done. When I put on the French kit, it's always a pleasure to represent my town, Boulogne-sur-Mer, which faces England. It's what I like to do, so I am very proud.'
In the men's K2, Sweden's Markus Oscarsson and Henrik Nilsson showed impressive form, while the Australian pair of Dave Smith and Ken Wallace also qualified comfortably.
The women's K4 semi-finals were dominated by the Germans and Hungarians.